Bibliography B

♦A♦B♦C♦D♦E♦F♦G♦H♦I♦J♦K♦L♦M♦N♦O♦P♦Q♦R♦S♦T♦U♦V♦W♦X♦Y♦Z♦

A. W. Babister (1967)
Transcendental Functions Satisfying Nonhomogeneous Linear Differential Equations,

The Macmillan Co., New York.

External Links:

MathReview (H. Hochstadt), ZentralBlatt.

Referenced by:

§11.4(i), §11.4(v), ¶ ‣ §11.5(ii), §11.5(i), §11.5(ii), §11.5(iii), §11.7(ii), §11.7(iii), §11.7(v), ¶ ‣ §11.9(i), §11.9(iv), §11.9(iv), Ch.11, §14.29.

Encodings:

BibTeX
L. V. Babushkina, M. K. Kerimov and A. I. Nikitin (1988a)
Algorithms for computing Bessel functions of half-integer order with complex arguments,

Zh. Vychisl. Mat. i Mat. Fiz. 28 (10), pp. 1449–1460, 1597.

Notes:

English translation in U.S.S.R. Comput. Math. and Math. Phys. 28(1988), no. 5, 109–117

External Links:

ISSN 0044-4669, Document, MathReview (Walter Gautschi), ZentralBlatt.

Referenced by:

§10.77(iv).

Encodings:

BibTeX
L. V. Babushkina, M. K. Kerimov and A. I. Nikitin (1988b)
Algorithms for evaluating spherical Bessel functions in the complex domain,

Zh. Vychisl. Mat. i Mat. Fiz. 28 (12), pp. 1779–1788, 1918.

Notes:

English translation in U.S.S.R. Comput. Math. and Math. Phys. 28(1988), no. 6, 122–128

External Links:

ISSN 0044-4669, Document, MathReview (Walter Gautschi), ZentralBlatt.

Referenced by:

§10.77(iv).

Encodings:

BibTeX
L. V. Babushkina, M. K. Kerimov and A. I. Nikitin (1997)
New tables of Bessel functions of complex argument,

Comput. Math. Math. Phys. 37 (12), pp. 1480–1482.

Notes:

Russian original in Zh. Vychisl. Mat. i Mat. Fiz. 37(1997), no. 12, 1526–1528

External Links:

ZentralBlatt.

Referenced by:

§10.75(i).

Encodings:

BibTeX
G. Backenstoss (1970)
Pionic atoms,

Annual Review of Nuclear and Particle Science 20, pp. 467–508.

External Links:

Document.

Referenced by:

§33.22(iv).

Encodings:

BibTeX
J. Baik, P. Deift and K. Johansson (1999)
On the distribution of the length of the longest increasing subsequence of random permutations,

J. Amer. Math. Soc. 12 (4), pp. 1119–1178.

External Links:

ISSN 0894-0347, FullText, MathReview (David J. Aldous), ZentralBlatt.

Referenced by:

§32.14.

Encodings:

BibTeX
D. H. Bailey (1993)
Algorithm 719: Multiprecision translation and execution of Fortran programs,

ACM Trans. Math. Software 19 (3), pp. 288–319.

External Links:

ISSN 0098-3500, Document, TOMS module 719 (in GAMS), C++ wrapper, ZentralBlatt.

Referenced by:

§4.48(iii), §5.24(ii).

Encodings:

BibTeX
D. H. Bailey (1995)
A Fortran-90 based multiprecision system,

ACM Trans. Math. Software 21 (4), pp. 379–387.

External Links:

ISSN 0098-3500, Document, ZentralBlatt.

Referenced by:

§4.48(iii).

Encodings:

BibTeX
W. N. Bailey (1928)
Products of generalized hypergeometric series,

Proc. London Math. Soc. (2) 28 (2), pp. 242–254.

External Links:

Document, ZentralBlatt.

Referenced by:

§16.12.

Encodings:

BibTeX
W. N. Bailey (1929)
Transformations of generalized hypergeometric series,

Proc. London Math. Soc. (2) 29 (2), pp. 495–502.

External Links:

Document, ZentralBlatt.

Referenced by:

§16.6.

Encodings:

BibTeX
W. N. Bailey (1935)
Generalized Hypergeometric Series,

Cambridge University Press, Cambridge.

Notes:

Reissued by Hafner, New York, 1972.

External Links:

ZentralBlatt.

Referenced by:

§17.1, §17.4(i), Ch.17.

Encodings:

BibTeX
W. N. Bailey (1964)
Generalized Hypergeometric Series,

Stechert-Hafner, Inc., New York.

External Links:

MathReview.

Referenced by:

§16.4(iii), §16.4(iii), §16.4(iii), §16.4(iii), §16.4(iii).

Encodings:

BibTeX
G. A. Baker and P. Graves-Morris (1996)
Padé Approximants,

2nd edition, Encyclopedia of Mathematics and its Applications, Vol. 59, Cambridge University Press, Cambridge.

External Links:

ISBN 0-521-45007-1, MathReview (Annie A. M. Cuyt), ZentralBlatt.

Referenced by:

¶ ‣ §3.11(iv), §3.11(iv).

Encodings:

BibTeX
H. F. Baker (1995)
Abelian Functions: Abel’s Theorem and the Allied Theory of Theta Functions,

Cambridge University Press, Cambridge.

Notes:

Reprint of the 1897 original, with a foreword by Igor Krichever.

External Links:

ISBN 0-521-49877-5, MathReview (John B. Little), ZentralBlatt.

Referenced by:

§20.9(ii).

Encodings:

BibTeX
L. Baker (1992)
C Mathematical Function Handbook,

McGraw-Hill, Inc., New York.

Notes:

Includes diskette containing a large collection of mathematical function software written in C; Double-precision, maximum accuracy 9S.

External Links:

ISBN 00-791-1158-0.

Referenced by:

§ ‣ § Software Cross Index.

Encodings:

BibTeX
P. Baldwin (1985)
Zeros of generalized Airy functions,

Mathematika 32 (1), pp. 104–117.

External Links:

ISSN 0025-5793, MathReview (M. E. Muldoon), ZentralBlatt.

Referenced by:

§9.13(ii).

Encodings:

BibTeX
P. Baldwin (1991)
Coefficient functions for an inhomogeneous turning-point problem,

Mathematika 38 (2), pp. 217–238.

External Links:

ISSN 0025-5793, MathReview (Archibald D. MacGillivray), ZentralBlatt.

Referenced by:

§2.8(iii).

Encodings:

BibTeX
J. S. Ball (2000)
Automatic computation of zeros of Bessel functions and other special functions,

SIAM J. Sci. Comput. 21 (4), pp. 1458–1464.

External Links:

ISSN 1064-8275, Document, MathReview (Andrea Laforgia), ZentralBlatt.

Referenced by:

¶ ‣ §10.74(vi), ¶ ‣ §3.8(iii).

Encodings:

BibTeX
L. E. Ballentine and S. M. McRae (1998)
Moment equations for probability distributions in classical and quantum mechanics,

Phys. Rev. A 58 (3), pp. 1799–1809.

External Links:

Document.

Referenced by:

§24.18.

Encodings:

BibTeX
C. B. Balogh (1967)
Asymptotic expansions of the modified Bessel function of the third kind of imaginary order,

SIAM J. Appl. Math. 15, pp. 1315–1323.

External Links:

ISSN 0036-1399, Document, MathReview (F. W. J. Olver), ZentralBlatt.

Referenced by:

§10.45.

Encodings:

BibTeX
E. Bannai (1990)
Orthogonal Polynomials in Coding Theory and Algebraic Combinatorics,

in Orthogonal Polynomials (Columbus, OH, 1989),

NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., Vol. 294, pp. 25–53.

External Links:

MathReview, ZentralBlatt.

Referenced by:

¶ ‣ §18.38(iii).

Encodings:

BibTeX
A. Bar-Shalom and M. Klapisch (1988)
NJGRAF: An efficient program for calculation of general recoupling coefficients by graphical analysis, compatible with NJSYM,

Comput. Phys. Comm. 50 (3), pp. 375–393.

External Links:

Document, Code.

Referenced by:

§34.15.

Encodings:

BibTeX
R. Barakat and E. Parshall (1996)
Numerical evaluation of the zero-order Hankel transform using Filon quadrature philosophy,

Appl. Math. Lett. 9 (5), pp. 21–26.

External Links:

ISSN 0893-9659, Document, MathReview, ZentralBlatt.

Referenced by:

¶ ‣ §10.74(vii).

Encodings:

BibTeX
R. Barakat (1961)
Evaluation of the incomplete gamma function of imaginary argument by Chebyshev polynomials,

Math. Comp. 15 (73), pp. 7–11.

External Links:

FullText, MathReview (J. C. P. Miller), ZentralBlatt.

Referenced by:

§8.7.

Encodings:

BibTeX
P. Baratella and L. Gatteschi (1988)
The Bounds for the Error Term of an Asymptotic Approximation of Jacobi Polynomials,

in Orthogonal Polynomials and Their Applications (Segovia, 1986),

Lecture Notes in Math., Vol. 1329, pp. 203–221.

External Links:

MathReview (F. W. J. Olver), ZentralBlatt.

Referenced by:

§18.15(i).

Encodings:

BibTeX
M. N. Barber and B. W. Ninham (1970)
Random and Restricted Walks: Theory and Applications.,

Gordon and Breach, New York.

External Links:

ZentralBlatt.

Referenced by:

§16.24(i).

Encodings:

BibTeX
C. Bardin, Y. Dandeu, L. Gauthier, J. Guillermin, T. Lena, J. M. Pernet, H. H. Wolter and T. Tamura (1972)
Coulomb functions in entire ( $\eta,\rho$ )-plane,

Comput. Phys. Comm. 3 (2), pp. 73–87.

External Links:

Document, Code.

Referenced by:

§33.23(vi).

Encodings:

BibTeX
R. W. Barnard, K. Pearce and K. C. Richards (2000)
A monotonicity property involving $\mathop{{{}_{{3}}F_{{2}}}\/}\nolimits$ and comparisons of the classical approximations of elliptical arc length,

SIAM J. Math. Anal. 32 (2), pp. 403–419.

External Links:

ISSN 1095-7154, Document, MathReview (Richard B. Paris), ZentralBlatt.

Referenced by:

§19.9(i), §19.9(i).

Encodings:

BibTeX
R. W. Barnard, K. Pearce and L. Schovanec (2001)
Inequalities for the perimeter of an ellipse,

J. Math. Anal. Appl. 260 (2), pp. 295–306.

External Links:

ISSN 0022-247X, Document, MathReview (Matti Vuorinen), ZentralBlatt.

Referenced by:

§19.9(i).

Encodings:

BibTeX
A. R. Barnett, D. H. Feng, J. W. Steed and L. J. B. Goldfarb (1974)
Coulomb wave functions for all real $\eta$ and $\rho$ ,

Comput. Phys. Comm. 8 (5), pp. 377–395.

Notes:

Single-precision Fortran code for positive energies. For modification see same journal, 11(1976), p. 141.

External Links:

Document, Code.

Referenced by:

§3.10(iii), §33.26(ii), §33.8.

Encodings:

BibTeX
A. R. Barnett (1981a)
An algorithm for regular and irregular Coulomb and Bessel functions of real order to machine accuracy,

Comput. Phys. Comm. 21 (3), pp. 297–314.

External Links:

Document.

Referenced by:

§3.10(iii), §33.22(iv).

Encodings:

BibTeX
A. R. Barnett (1981b)
KLEIN: Coulomb functions for real $\lambda$ and positive energy to high accuracy,

Comput. Phys. Comm. 24 (2), pp. 141–159.

Notes:

Double-precision Fortran code for positive energies.

External Links:

Document, Code.

Referenced by:

§33.22(vii), §33.23(vii), §33.26(ii).

Encodings:

BibTeX
A. R. Barnett (1982)
COULFG: Coulomb and Bessel functions and their derivatives, for real arguments, by Steed’s method,

Comput. Phys. Comm. 27, pp. 147–166.

Notes:

Double-precision Fortran code for positive energies. Maximum accuracy: 31S.

External Links:

Document, Code.

Referenced by:

§10.77(iii), §33.26(ii).

Encodings:

BibTeX
A. R. Barnett (1996)
The Calculation of Spherical Bessel Functions and Coulomb Functions,

in Computational Atomic Physics: Electron and Positron Collisions with Atoms and Ions,

(J. Hinze Ed.), pp. 181–202.

Notes:

Includes program disk. Double-precision Fortran code for positive energies. Maximum accuracy: 15D.

External Links:

ISBN 3-540-60179-1, FullText and Code.

Referenced by:

§33.26(ii), §33.8.

Encodings:

BibTeX
E. Barouch, B. M. McCoy and T. T. Wu (1973)
Zero-field susceptibility of the two-dimensional Ising model near $T_{c}$ ,

Phys. Rev. Lett. 31, pp. 1409–1411.

External Links:

Document.

Referenced by:

¶ ‣ §32.16.

Encodings:

BibTeX
G. E. Barr (1968)
A note on integrals involving parabolic cylinder functions,

SIAM J. Appl. Math. 16 (1), pp. 71–74.

External Links:

Document, MathReview (T. Erber), ZentralBlatt.

Referenced by:

¶ ‣ §12.12.

Encodings:

BibTeX
R. F. Barrett (1964)
Tables of modified Struve functions of orders zero and unity,

Notes:

Part of the Unpublished Mathematical Tables. Reviewed in Math. Comp., v. 18 (1964), no. 86, p. 332.

Referenced by:

§11.14(ii).

Encodings:

BibTeX
W. Barrett (1981)
Mathieu functions of general order: Connection formulae, base functions and asymptotic formulae. I–V,

Philos. Trans. Roy. Soc. London Ser. A 301, pp. 75–162.

External Links:

ISSN 0080-4614, FullText, MathReview (J. Meixner), ZentralBlatt.

Referenced by:

¶ ‣ §28.8(iv).

Encodings:

BibTeX
P. Barrucand and D. Dickinson (1968)
On the Associated Legendre Polynomials,

in Orthogonal Expansions and their Continuous Analogues (Proc. Conf., Edwardsville, Ill., 1967),

pp. 43–50.

External Links:

MathReview (B. R. Bhonsle), ZentralBlatt.

Referenced by:

§18.30.

Encodings:

BibTeX
D. A. Barry, S. J. Barry and P. J. Culligan-Hensley (1995a)
Algorithm 743: WAPR: A Fortran routine for calculating real values of the $W$ -function,

ACM Trans. Math. Software 21 (2), pp. 172–181.

External Links:

ISSN 0098-3500, Document, TOMS module 743 (in GAMS), MathReview Entry, ZentralBlatt.

Referenced by:

§4.48(iv).

Encodings:

BibTeX
D. A. Barry, P. J. Culligan-Hensley and S. J. Barry (1995b)
Real values of the $W$ -function,

ACM Trans. Math. Software 21 (2), pp. 161–171.

External Links:

ISSN 0098-3500, Document, MathReview Entry, ZentralBlatt.

Referenced by:

§4.45(iii).

Encodings:

BibTeX
W. Bartky (1938)
Numerical calculation of a generalized complete elliptic integral,

Rev. Mod. Phys. 10, pp. 264–269.

External Links:

Document, ZentralBlatt.

Referenced by:

§19.2(iii).

Encodings:

BibTeX
A. O. Barut and L. Girardello (1971)
New “coherent” states associated with non-compact groups,

Comm. Math. Phys. 21 (1), pp. 41–55.

External Links:

ISSN 0010-3616, MathReview (R. Mirman), ZentralBlatt.

Referenced by:

§13.28(iii).

Encodings:

BibTeX
A. P. Bassom, P. A. Clarkson, A. C. Hicks and J. B. McLeod (1992)
Integral equations and exact solutions for the fourth Painlevé equation,

Proc. Roy. Soc. London Ser. A 437, pp. 1–24.

External Links:

ISSN 0962-8444, FullText, MathReview (Mehmet Can), ZentralBlatt.

Referenced by:

§32.11(v), §32.2(iii).

Encodings:

BibTeX
A. P. Bassom, P. A. Clarkson and A. C. Hicks (1993)
Numerical studies of the fourth Painlevé equation,

IMA J. Appl. Math. 50 (2), pp. 167–193.

External Links:

ISSN 0272-4960, Document, MathReview, ZentralBlatt.

Referenced by:

§32.17, §32.3(iii).

Encodings:

BibTeX
A. P. Bassom, P. A. Clarkson and A. C. Hicks (1995)
Bäcklund transformations and solution hierarchies for the fourth Painlevé equation,

Stud. Appl. Math. 95 (1), pp. 1–71.

External Links:

ISSN 0022-2526, MathReview (Andrei A. Kapaev), ZentralBlatt.

Referenced by:

§32.10(iv), §32.2(iii), §32.7(iv), §32.8(iv).

Encodings:

BibTeX
A. P. Bassom, P. A. Clarkson, C. K. Law and J. B. McLeod (1998)
Application of uniform asymptotics to the second Painlevé transcendent,

Arch. Rational Mech. Anal. 143 (3), pp. 241–271.

External Links:

ISSN 0945-8396, Document, MathReview (Andrei A. Kapaev), ZentralBlatt.

Referenced by:

§32.11(ii).

Encodings:

BibTeX
A. Basu and T. M. Apostol (2000)
A new method for investigating Euler sums,

Ramanujan J. 4 (4), pp. 397–419.

External Links:

ISSN 1382-4090, Document, MathReview (Bruce C. Berndt), ZentralBlatt.

Referenced by:

§25.16(ii), §25.6(iii), §25.6(iii).

Encodings:

BibTeX
P. M. Batchelder (1967)
An Introduction to Linear Difference Equations,

Dover Publications Inc., New York.

Notes:

Unaltered republication of the original 1927 Harvard University edition.

External Links:

MathReview, ZentralBlatt.

Referenced by:

§8.1.

Encodings:

BibTeX
H. Bateman (1905)
A generalisation of the Legendre polynomial,

Proc. London Math. Soc. (2) 3 (3), pp. 111–123.

Notes:

Reviewed in JFM 36.0512.01

External Links:

Document, ZentralBlatt.

Referenced by:

§18.12.

Encodings:

BibTeX
H. Bateman and R. C. Archibald (1944)
A guide to tables of Bessel functions,

Mathematical Tables and Other Aids to Computation (now Mathematics of Computation) 1 (7), pp. 205–308.

External Links:

FullText, MathReview (G. Szegö), ZentralBlatt.

Referenced by:

§10.75(i).

Encodings:

BibTeX
F. L. Bauer, H. Rutishauser and E. Stiefel (1963)
New Aspects in Numerical Quadrature,

in Proc. Sympos. Appl. Math., Vol. XV,

pp. 199–218.

External Links:

MathReview (S. Haber), ZentralBlatt.

Referenced by:

§3.5(iii).

Encodings:

BibTeX
G. Baxter (1961)
Polynomials defined by a difference system,

J. Math. Anal. Appl. 2 (2), pp. 223–263.

External Links:

Document, MathReview (F. L. Spitzer), ZentralBlatt.

Referenced by:

§18.33(v).

Encodings:

BibTeX
R. J. Baxter (1981)
Rogers-Ramanujan identities in the hard hexagon model,

J. Statist. Phys. 26 (3), pp. 427–452.

External Links:

ISSN 0022-4715, Document, MathReview, ZentralBlatt.

Referenced by:

§17.17.

Encodings:

BibTeX
R. J. Baxter (1982)
Exactly Solved Models in Statistical Mechanics,

Academic Press Inc., London-New York.

Notes:

Reprinted in 1989.

External Links:

ISBN 0-12-083180-5, MathReview (J. Groeneveld), ZentralBlatt.

Referenced by:

§17.17, §20.12(ii), §22.18(iii), §23.21(iv), §26.20.

Encodings:

BibTeX
K. Bay, W. Lay and A. Akopyan (1997)
Avoided crossings of the quartic oscillator,

J. Phys. A 30 (9), pp. 3057–3067.

External Links:

ISSN 0305-4470, Document, MathReview (Gabriel Alvarez), ZentralBlatt.

Referenced by:

§31.17(ii).

Encodings:

BibTeX
C. Bays and R. H. Hudson (2000)
A new bound for the smallest $x$ with $\pi(x)>{\rm li}(x)$ ,

Math. Comp. 69 (231), pp. 1285–1296.

External Links:

ISSN 0025-5718, Document, MathReview, ZentralBlatt.

Referenced by:

¶ ‣ §27.12, §6.16(ii).

Encodings:

BibTeX
L. P. Bayvel and A. R. Jones (1981)
Electromagnetic Scattering and its Applications,

Applied Science Publishers, London.

External Links:

ISBN 0-85334-955-X.

Referenced by:

§10.73(i), §10.73(ii).

Encodings:

BibTeX
A. Bañuelos, R. A. Depine and R. C. Mancini (1981)
A program for computing the Fermi-Dirac functions,

Comput. Phys. Comm. 21 (3), pp. 315–322.

Notes:

Double-precision Fortran, maximum accuracy 10D.

External Links:

Document, Code.

Referenced by:

§25.21(vii).

Encodings:

BibTeX
A. Bañuelos and R. A. Depine (1980)
A program for computing the Riemann zeta function for complex argument,

Comput. Phys. Comm. 20 (3), pp. 441–445.

Notes:

Double-precision Fortran, maximum accuracy 10S.

External Links:

Document, Code, ZentralBlatt.

Referenced by:

§25.21(iii).

Encodings:

BibTeX
E. F. Beckenbach (Ed.) (1981)
Applied Combinatorial Mathematics,

Robert E. Krieger, Malabar, FL.

External Links:

ZentralBlatt.

Referenced by:

§26.19, §26.20.

Encodings:

BibTeX
P. A. Becker (1997)
Normalization integrals of orthogonal Heun functions,

J. Math. Phys. 38 (7), pp. 3692–3699.

External Links:

ISSN 0022-2488, Document, MathReview, ZentralBlatt.

Referenced by:

§31.9(i).

Encodings:

BibTeX
R. Becker and F. Sauter (1964)
Electromagnetic Fields and Interactions,

Vol. I, Blaisdell, New York.

Notes:

Replaces Abraham & Becker, Classical Theory of Electricity and Magnetism.

Referenced by:

§19.33(iii), §19.34.

Encodings:

BibTeX
P. Beckmann and A. Spizzichino (1963)
The Scattering of Electromagnetic Waves from Rough Surfaces,

Pergamon Press, New York.

Notes:

Reprinted in 1987 by Artech House Publishers, Norwood, Massachusetts.

External Links:

ISBN 0-89006-238-2, ZentralBlatt.

Referenced by:

§10.73(i).

Encodings:

BibTeX
V. M. Beli͡akov, R. I. Kravt͡sova and M. G. Rappoport (1962)
Tablit͡sy Elliptic͡heskik͡h Integralov. Tom I,

Mathematical tables of the Computing Center of the Academy of Sciences of the USSR], Izdat. Akad. Nauk SSSR, Moscow (Russian).

Notes:

Reviewed in Math. Comp. v. 18(1964), pp. 676–677.

External Links:

MathReview (John Todd), ZentralBlatt.

Referenced by:

¶ ‣ §19.37(ii), ¶ ‣ §19.37(iii), ¶ ‣ §19.37(iii).

Encodings:

BibTeX
K. L. Bell and N. S. Scott (1980)
Coulomb functions (negative energies),

Comput. Phys. Comm. 20 (3), pp. 447–458.

Notes:

Double-precision Fortran code.

External Links:

Document, Code.

Referenced by:

§13.32(ii), §33.26(ii).

Encodings:

BibTeX
R. Bellman (1961)
A Brief Introduction to Theta Functions,

Athena Series: Selected Topics in Mathematics, Holt, Rinehart and Winston, New York.

External Links:

MathReview (W. J. LeVeque), ZentralBlatt.

Referenced by:

§20.10(i), §20.10(ii), §20.11(i), §20.13, §20.5(ii), §20.7(viii), §20.8.

Encodings:

BibTeX
E. D. Belokolos, A. I. Bobenko, V. Z. Enol’skii, A. R. Its and V. B. Matveev (1994)
Algebro-geometric Approach to Nonlinear Integrable Problems,

Springer Series in Nonlinear Dynamics, Springer-Verlag, Berlin.

External Links:

ISBN 3-540-50265-3, ZentralBlatt.

Referenced by:

§21.1, §21.10(ii), §21.6(ii), §21.7(i), §21.7(i), §21.9, Ch.21, Alexander I. Bobenko, Alexander A. Its.

Encodings:

BibTeX
S. L. Belousov (1962)
Tables of Normalized Associated Legendre Polynomials,

Pergamon Press, The Macmillan Co., Oxford-New York.

External Links:

MathReview (F. W. J. Olver), ZentralBlatt.

Referenced by:

§14.33.

Encodings:

BibTeX
C. M. Bender and S. A. Orszag (1978)
Advanced Mathematical Methods for Scientists and Engineers,

McGraw-Hill Book Co., New York.

Notes:

Reprinted by Springer-Verlag, New York, 1999.

External Links:

ISBN 0-07-004452-X; 0-387-98931-5, MathReview (Vadim Komkov), ZentralBlatt.

Referenced by:

§32.11(i).

Encodings:

BibTeX
C. M. Bender and T. T. Wu (1973)
Anharmonic oscillator. II. A study of perturbation theory in large order,

Phys. Rev. D 7, pp. 1620–1636.

External Links:

Document.

Referenced by:

§22.19(ii).

Encodings:

BibTeX
E. A. Bender (1974)
Asymptotic methods in enumeration,

SIAM Rev. 16 (4), pp. 485–515.

External Links:

Document, MathReview (Bernard Harris), ZentralBlatt.

Referenced by:

Ch.2.

Encodings:

BibTeX
P. Berglund, P. Candelas, X. de la Ossa and et al. (1994)
Periods for Calabi-Yau and Landau-Ginzburg vacua,

Nuclear Phys. B 419 (2), pp. 352–403.

External Links:

ISSN 0550-3213, Document, MathReview (Bruce Hunt), ZentralBlatt.

Referenced by:

§16.23(i).

Encodings:

BibTeX
A. Berkovich and B. M. McCoy (1998)
Rogers-Ramanujan Identities: A Century of Progress from Mathematics to Physics,

pp. 163–172.

External Links:

ISSN 1431-0643, FullText, MathReview (Anne Schilling), ZentralBlatt.

Referenced by:

§17.17.

Encodings:

BibTeX
G. D. Bernard and A. Ishimaru (1962)
Tables of the Anger and Lommel-Weber Functions,

Technical report

Technical Report 53 and AFCRL 796, University Washington Press, Seattle.

Notes:

Reviewed in Math. Comp., v. 17 (1963), pp.315–317.

Referenced by:

§11.14(iv).

Encodings:

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B. C. Berndt, S. Bhargava and F. G. Garvan (1995)
Ramanujan’s theories of elliptic functions to alternative bases,

Trans. Amer. Math. Soc. 347 (11), pp. 4163–4244.

External Links:

ISSN 0002-9947, FullText, MathReview (J. Borwein), ZentralBlatt.

Referenced by:

¶ ‣ §15.8(v), §20.11(iii).

Encodings:

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B. C. Berndt and R. J. Evans (1984)
Chapter 13 of Ramanujan’s second notebook: Integrals and asymptotic expansions,

Expo. Math. 2 (4), pp. 289–347.

External Links:

ISSN 0723-0869, MathReview (F. W. J. Olver), ZentralBlatt.

Referenced by:

¶ ‣ §2.10(iii).

Encodings:

BibTeX
B. C. Berndt (1972)
On the Hurwitz zeta-function,

Rocky Mountain J. Math. 2 (1), pp. 151–157.

External Links:

MathReview (K. Thanigasalam), ZentralBlatt.

Referenced by:

§25.11(vii).

Encodings:

BibTeX
B. C. Berndt (1975a)
Character analogues of the Poisson and Euler-MacLaurin summation formulas with applications,

J. Number Theory 7 (4), pp. 413–445.

External Links:

Document, MathReview (T. M. Apostol), ZentralBlatt.

Referenced by:

§24.16(ii).

Encodings:

BibTeX
B. C. Berndt (1975b)
Periodic Bernoulli numbers, summation formulas and applications,

in Theory and Application of Special Functions (Proc. Advanced Sem., Math. Res. Center, Univ. Wisconsin, Madison, Wis., 1975),

pp. 143–189.

External Links:

MathReview (L. Carlitz), ZentralBlatt.

Referenced by:

§24.16(iii), §24.8(ii).

Encodings:

BibTeX
B. C. Berndt (1989)
Ramanujan’s Notebooks. Part II,

Springer-Verlag, New York.

External Links:

ISBN 0-387-96794-X, MathReview (R. A. Askey), ZentralBlatt.

Referenced by:

§15.7.

Encodings:

BibTeX
B. C. Berndt (1991)
Ramanujan’s Notebooks. Part III,

Springer-Verlag, Berlin-New York.

External Links:

ISBN 0-387-97503-9, MathReview (R. A. Askey), ZentralBlatt.

Referenced by:

§17.13.

Encodings:

BibTeX
K. A. Berrington, P. G. Burke, J. J. Chang., A. T. Chivers, W. D. Robb and K. T. Taylor (1974)
A general program to calculate atomic continuum processes using the R-matrix method,

Comput. Phys. Comm. 8 (3), pp. 149–198.

External Links:

Document, Code.

Referenced by:

§34.15.

Encodings:

BibTeX
M. V. Berry and C. J. Howls (1990)
Stokes surfaces of diffraction catastrophes with codimension three,

Nonlinearity 3 (2), pp. 281–291.

External Links:

ISSN 0951-7715, Document, MathReview (Maria Carmen Romero-Fuster), ZentralBlatt.

Referenced by:

§36.2(i), §36.5(ii), §36.5(iii), §36.5(iv).

Encodings:

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M. V. Berry and C. J. Howls (1991)
Hyperasymptotics for integrals with saddles,

Proc. Roy. Soc. London Ser. A 434, pp. 657–675.

External Links:

ISSN 0962-8444, FullText, MathReview (Andreas Guthmann), ZentralBlatt.

Referenced by:

§2.11(v), §36.11.

Encodings:

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M. V. Berry and C. J. Howls (1993)
Unfolding the high orders of asymptotic expansions with coalescing saddles: Singularity theory, crossover and duality,

Proc. Roy. Soc. London Ser. A 443, pp. 107–126.

External Links:

ISSN 0962-8444, FullText, MathReview (Roderick Wong), ZentralBlatt.

Referenced by:

§36.12(i), §36.12(ii), §36.12(iii).

Encodings:

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M. V. Berry and C. J. Howls (1994)
Overlapping Stokes smoothings: Survival of the error function and canonical catastrophe integrals,

Proc. Roy. Soc. London Ser. A 444, pp. 201–216.

External Links:

ISSN 0962-8444, FullText, MathReview (F. Ursell), ZentralBlatt.

Referenced by:

§36.12(iii).

Encodings:

BibTeX
M. V. Berry and C. J. Howls (2010)
Axial and focal-plane diffraction catastrophe integrals,

J. Phys. A 43 (Art. ID 375206, 13 pages).

External Links:

ISSN 1751-8113, Document, FullText, MathReview (Andrei A. Kapaev), ZentralBlatt.

Referenced by:

(36.2.28), (36.2.29), §36.2(iv).

Encodings:

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M. V. Berry and J. P. Keating (1992)
A new asymptotic representation for $\zeta(\frac{1}{2}+it)$ and quantum spectral determinants,

Proc. Roy. Soc. London Ser. A 437, pp. 151–173.

External Links:

ISSN 0962-8444, MathReview (Jack Quine), ZentralBlatt.

Referenced by:

§25.9.

Encodings:

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M. V. Berry and J. P. Keating (1998)
$H=xp$ and the Riemann Zeros,

in Supersymmetry and Trace Formulae: Chaos and Disorder,

(J. P. Keating and D. E. Khmelnitskii Eds.), pp. 355–367.

External Links:

ISBN 0306459337.

Referenced by:

§25.17.

Encodings:

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M. V. Berry and J. P. Keating (1999)
The Riemann zeros and eigenvalue asymptotics,

SIAM Rev. 41 (2), pp. 236–266.

External Links:

ISSN 1095-7200, Document, MathReview (Richard B. Paris), ZentralBlatt.

Referenced by:

§25.17.

Encodings:

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M. V. Berry, J. F. Nye and F. J. Wright (1979)
The elliptic umbilic diffraction catastrophe,

Phil. Trans. Roy. Soc. Ser. A 291 (1382), pp. 453–484.

External Links:

FullText.

Referenced by:

§36.15(iv), §36.2(i), §36.7(ii), §36.7(iii).

Encodings:

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M. V. Berry and C. Upstill (1980)
Catastrophe optics: Morphologies of caustics and their diffraction patterns,

in Progress in Optics,

Vol. 18, pp. 257–346.

Referenced by:

§36.14(ii), Ch.36.

Encodings:

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M. V. Berry and F. J. Wright (1980)
Phase-space projection identities for diffraction catastrophes,

J. Phys. A 13 (1), pp. 149–160.

External Links:

ISSN 0305-4470, Document, MathReview (J. S. Joel), ZentralBlatt.

Referenced by:

§36.9.

Encodings:

BibTeX
M. V. Berry (1966)
Uniform approximation for potential scattering involving a rainbow,

Proc. Phys. Soc. 89 (3), pp. 479–490.

External Links:

Document, ZentralBlatt.

Referenced by:

§36.14(iii), §9.16.

Encodings:

BibTeX
M. V. Berry (1969)
Uniform approximation: A new concept in wave theory,

Science Progress (Oxford) 57, pp. 43–64.

Referenced by:

§36.14(i), §9.16.

Encodings:

BibTeX
M. V. Berry (1975)
Cusped rainbows and incoherence effects in the rippling-mirror model for particle scattering from surfaces,

J. Phys. A 8 (4), pp. 566–584.

External Links:

Document, MathReview.

Referenced by:

§36.14(iii).

Encodings:

BibTeX
M. V. Berry (1976)
Waves and Thom’s theorem,

Advances in Physics 25 (1), pp. 1–26.

External Links:

Document.

Referenced by:

§36.14(i).

Encodings:

BibTeX
M. V. Berry (1977)
Focusing and twinkling: Critical exponents from catastrophes in non-Gaussian random short waves,

J. Phys. A 10 (12), pp. 2061–2081.

External Links:

Document, MathReview, ZentralBlatt.

Referenced by:

¶ ‣ §36.6.

Encodings:

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M. V. Berry (1980)
Some Geometric Aspects of Wave Motion: Wavefront Dislocations, Diffraction Catastrophes, Diffractals,

in Geometry of the Laplace Operator (Proc. Sympos. Pure Math., Univ. Hawaii, Honolulu, Hawaii, 1979),

Vol. 36, pp. 13–28.

External Links:

MathReview (I. Stewart), ZentralBlatt.

Referenced by:

§36.14(i).

Encodings:

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M. V. Berry (1981)
Singularities in Waves and Rays,

in Les Houches Lecture Series Session XXXV,

(M. Kléman and J.-P. Poirier Eds.), Vol. 35, pp. 453–543.

Referenced by:

§36.14(i).

Encodings:

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M. V. Berry (1989)
Uniform asymptotic smoothing of Stokes’s discontinuities,

Proc. Roy. Soc. London Ser. A 422, pp. 7–21.

External Links:

ISSN 0080-4630, FullText, MathReview (André Hautot), ZentralBlatt.

Referenced by:

§2.11(iv).

Encodings:

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M. V. Berry (1991)
Infinitely many Stokes smoothings in the gamma function,

Proc. Roy. Soc. London Ser. A 434, pp. 465–472.

External Links:

ISSN 0962-8444, FullText, MathReview (E. Riekstiņš), ZentralBlatt.

Referenced by:

§5.11(ii).

Encodings:

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M. V. Berry (1995)
The Riemann-Siegel expansion for the zeta function: High orders and remainders,

Proc. Roy. Soc. London Ser. A 450, pp. 439–462.

External Links:

ISSN 0962-8444, FullText, MathReview (Christian Grosche), ZentralBlatt.

Referenced by:

§25.10(ii), §25.9.

Encodings:

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E. Berti and V. Cardoso (2006)
Quasinormal ringing of Kerr black holes: The excitation factors,

Phys. Rev. D 74 (104020), pp. 1–27.

External Links:

ISSN 0556-2821, Document, MathReview.

Referenced by:

§33.22(vii).

Encodings:

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H. A. Bethe and E. E. Salpeter (1977)
Quantum Mechanics of One- and Two-electron Atoms,

Rosetta edition, Plenum Publishing Corp., New York.

Notes:

Reprint (with corrections) of the original edition published in 1957 by Springer and Academic Press

External Links:

MathReview, ZentralBlatt (D. Geissler).

Referenced by:

¶ ‣ §33.22(ii), ¶ ‣ §33.22(ii), §33.22(v).

Encodings:

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F. Bethuel (1998)
Vortices in Ginzburg-Landau Equations,

pp. 11–19.

External Links:

ISSN 1431-0643, FullText, MathReview Entry, ZentralBlatt.

Referenced by:

§17.17.

Encodings:

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T. A. Beu and R. I. Câmpeanu (1983a)
Prolate angular spheroidal wave functions,

Comput. Phys. Comm. 30 (2), pp. 187–192.

External Links:

Document, Code.

Referenced by:

§30.18(iii).

Encodings:

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T. A. Beu and R. I. Câmpeanu (1983b)
Prolate radial spheroidal wave functions,

Comput. Phys. Comm. 30 (2), pp. 177–185.

External Links:

Document, Code.

Referenced by:

§30.18(iii).

Encodings:

BibTeX
V. Bezvoda, R. Farzan, K. Segeth and G. Takó (1986)
On numerical evaluation of integrals involving Bessel functions,

Apl. Mat. 31 (5), pp. 396–410.

External Links:

ISSN 0373-6725, MathReview (G. A. Evans), ZentralBlatt.

Referenced by:

¶ ‣ §10.74(vii).

Encodings:

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A. Bhattacharjie and E. C. G. Sudarshan (1962)
A class of solvable potentials,

Nuovo Cimento (10) 25, pp. 864–879.

External Links:

Document, MathReview (S. Rosendorff), ZentralBlatt.

Referenced by:

§15.18.

Encodings:

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A. Bhattacharyya and L. Shafai (1988)
Theoretical and experimental investigation of the elliptical annual ring antenna,

IEEE Trans. Antennas and Propagation 36 (11), pp. 1526–1530.

External Links:

Document.

Referenced by:

§28.33(ii).

Encodings:

BibTeX
D. K. Bhaumik and S. K. Sarkar (2002)
On the power function of the likelihood ratio test for MANOVA,

J. Multivariate Anal. 82 (2), pp. 416–421.

External Links:

ISSN 0047-259X, Document, MathReview (Yasuko Chikuse), ZentralBlatt.

Referenced by:

§35.9.

Encodings:

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W. G. Bickley, L. J. Comrie, J. C. P. Miller, D. H. Sadler and A. J. Thompson (1952)
Bessel Functions. Part II: Functions of Positive Integer Order,

British Association for the Advancement of Science, Mathematical Tables, Volume 10, Cambridge University Press, Cambridge.

Notes:

Reprinted, with corrections, in 1960.

External Links:

ISBN 0-521-04321-2, MathReview (R. C. Archibald), ZentralBlatt.

Referenced by:

§10.18(iii), §10.19(ii), §10.21(vi), §10.41(ii), §10.75(ii), §10.75(v), §3.6(iii).

Encodings:

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W. G. Bickley and J. Nayler (1935)
A short table of the functions $\mathrm{Ki}_{n}(x)$ , from $n=1$ to $n=16$ ,

Phil. Mag. Series 7 20, pp. 343–347.

External Links:

Document, ZentralBlatt.

Referenced by:

§10.43(iii), §10.75(vii).

Encodings:

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W. G. Bickley (1935)
Some solutions of the problem of forced convection.,

Philos. Mag. Series 7 20, pp. 322–343.

External Links:

Document, ZentralBlatt.

Referenced by:

§10.73(iv).

Encodings:

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L. C. Biedenharn, R. L. Gluckstern, M. H. Hull and G. Breit (1955)
Coulomb functions for large charges and small velocities,

Phys. Rev. (2) 97 (2), pp. 542–554.

External Links:

Document, MathReview (A. Erdélyi), ZentralBlatt.

Referenced by:

§33.5(iv).

Encodings:

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L. C. Biedenharn and J. D. Louck (1981)
Angular Momentum in Quantum Physics: Theory and Application,

Encyclopedia of Mathematics and its Applications, Vol. 8, Addison-Wesley Publishing Co., Reading, MA..

External Links:

ISBN 0-201-13507-8, MathReview (Kurt Bernardo Wolf), ZentralBlatt.

Referenced by:

§34.14.

Encodings:

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L. C. Biedenharn and H. van Dam (Eds.) (1965)
Quantum Theory of Angular Momentum. A Collection of Reprints and Original Papers,

Academic Press, New York.

External Links:

ISBN 0-12-096056-7, MathReview (R. Mirman).

Referenced by:

§34.12, §34.3(v), §34.5(v), §34.7(v).

Encodings:

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D. Bierens de Haan (1867)
Nouvelles Tables d’Intégrales Définies,

P. Engels, Leide.

Notes:

Corrected edition printed by Hafner Press, 1965.

Referenced by:

¶ ‣ §1.4(iv).

Encodings:

BibTeX

D. Bierens de Haan (1939)
Nouvelles Tables d’Intégrales Définies,

G.E. Stechert & Co., New York.

Referenced by:

§4.10(iii), §4.26(v), §4.40(v), §6.14(iii), §6.7(iv).

Encodings:

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L. J. Billera, C. Greene, R. Simion and R. P. Stanley (Eds.) (1996)
Formal Power Series and Algebraic Combinatorics,

DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Vol. 24, American Mathematical Society, Providence, RI.

External Links:

ISBN 0-8218-0324-7, MathReview, ZentralBlatt.

Referenced by:

§26.19.

Encodings:

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C. Bingham, T. Chang and D. Richards (1992)
Approximating the matrix Fisher and Bingham distributions: Applications to spherical regression and Procrustes analysis,

J. Multivariate Anal. 41 (2), pp. 314–337.

External Links:

ISSN 0047-259X, Document, MathReview (A. L. Rukhin), ZentralBlatt.

Referenced by:

§35.10, §35.9.

Encodings:

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R. L. Bishop (1981)
Rainbow over Woolsthorpe Manor,

Notes and Records Roy. Soc. London 36 (1), pp. 3–11 (1 plate).

External Links:

ISSN 0035-9149, Document, MathReview.

Referenced by:

Sidebar 9.SB1.

Encodings:

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Å. Björck (1996)
Numerical Methods for Least Squares Problems,

Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.

External Links:

ISBN 0-89871-360-9, MathReview (Hongyuan Zha), ZentralBlatt.

Referenced by:

¶ ‣ §3.11(v).

Encodings:

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J. M. Blair, C. A. Edwards and J. H. Johnson (1976)
Rational Chebyshev approximations for the inverse of the error function,

Math. Comp. 30 (136), pp. 827–830.

External Links:

FullText, MathReview, ZentralBlatt.

Referenced by:

§7.17(iii).

Encodings:

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J. M. Blair, C. A. Edwards and J. H. Johnson (1978)
Rational Chebyshev approximations for the Bickley functions $Ki_{{n}}(x)$ ,

Math. Comp. 32 (143), pp. 876–886.

External Links:

ISSN 0025-5718, FullText, MathReview (H. Hochstadt), ZentralBlatt.

Referenced by:

¶ ‣ §10.76(iii).

Encodings:

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G. Blanch and D. S. Clemm (1962)
Tables Relating to the Radial Mathieu Functions. Vol. 1: Functions of the First Kind,

U.S. Government Printing Office, Washington, D.C..

External Links:

MathReview (C. J. Bouwkamp).

Referenced by:

§28.35(i).

Encodings:

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G. Blanch and D. S. Clemm (1965)
Tables Relating to the Radial Mathieu Functions. Vol. 2: Functions of the Second Kind,

U.S. Government Printing Office, Washington, D.C..

External Links:

MathReview (C. J. Bouwkamp).

Referenced by:

§28.35(i), §28.35(iii).

Encodings:

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G. Blanch and D. S. Clemm (1969)
Mathieu’s Equation for Complex Parameters. Tables of Characteristic Values,

U.S. Government Printing Office, Washington, D.C..

External Links:

MathReview (John Todd), ZentralBlatt.

Referenced by:

§28.35(ii).

Encodings:

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G. Blanch (1964)
Numerical evaluation of continued fractions,

SIAM Rev. 6 (4), pp. 383–421.

External Links:

Document, MathReview (E. Frank), ZentralBlatt.

Referenced by:

¶ ‣ §3.10(iii), §3.10(ii).

Encodings:

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G. Blanch and I. Rhodes (1955)
Table of characteristic values of Mathieu’s equation for large values of the parameter,

J. Washington Acad. Sci. 45 (6), pp. 166–196.

External Links:

MathReview (L. Fox).

Referenced by:

§28.35(i).

Encodings:

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G. Blanch (1966)
Numerical aspects of Mathieu eigenvalues,

Rend. Circ. Mat. Palermo (2) 15, pp. 51–97.

External Links:

Document, MathReview (J. Meixner), ZentralBlatt.

Referenced by:

§28.34(ii).

Encodings:

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P. Bleher and A. Its (1999)
Semiclassical asymptotics of orthogonal polynomials, Riemann-Hilbert problem, and universality in the matrix model,

Ann. of Math. (2) 150 (1), pp. 185–266.

External Links:

ISSN 0003-486X, Document, MathReview (Thomas Kriecherbauer), ZentralBlatt.

Referenced by:

§18.32.

Encodings:

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D. Bleichenbacher (1996)
Efficiency and Security of Cryptosystems Based on Number Theory,

Ph.D. Thesis, Swiss Federal Institute of Technology (ETH), Zurich.

External Links:

FullText.

Referenced by:

§27.22.

Encodings:

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W. E. Bleick and P. C. C. Wang (1974)
Asymptotics of Stirling numbers of the second kind,

Proc. Amer. Math. Soc. 42 (2), pp. 575–580.

Notes:

Erratum: same journal v. 48 (1975), p. 518

External Links:

FullText, MathReview (H. A. Lauwerier), ZentralBlatt.

Referenced by:

§26.8(vii).

Encodings:

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N. Bleistein and R. A. Handelsman (1975)
Asymptotic Expansions of Integrals,

Holt, Rinehart, and Winston, New York.

Notes:

Reprinted with corrections by Dover Publications Inc., New York, 1986

External Links:

ISBN 0-486-65082-0, MathReview, ZentralBlatt.

Referenced by:

§2.3(v), §2.4(iv), §2.4(v), ¶ ‣ §2.5(iii), §2.5(ii), Ch.2, Ch.9.

Encodings:

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N. Bleistein (1966)
Uniform asymptotic expansions of integrals with stationary point near algebraic singularity,

Comm. Pure Appl. Math. 19, pp. 353–370.

External Links:

Document, MathReview (J. G. van der Corput), ZentralBlatt.

Referenced by:

§2.3(v).

Encodings:

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N. Bleistein (1967)
Uniform asymptotic expansions of integrals with many nearby stationary points and algebraic singularities,

J. Math. Mech. 17, pp. 533–559.

External Links:

MathReview (A. Erdélyi), ZentralBlatt.

Referenced by:

§36.12(iii).

Encodings:

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I. Bloch, M. H. Hull, A. A. Broyles, W. G. Bouricius, B. E. Freeman and G. Breit (1950)
Methods of calculation of radial wave functions and new tables of Coulomb functions,

Physical Rev. (2) 80, pp. 553–560.

External Links:

Document, MathReview (S. C. van Veen), ZentralBlatt.

Referenced by:

§33.7.

Encodings:

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I. Bloch, M. H. Hull, A. A. Broyles, W. G. Bouricius, B. E. Freeman and G. Breit (1951)
Coulomb functions for reactions of protons and alpha-particles with the lighter nuclei,

Rev. Modern Physics 23 (2), pp. 147–182.

External Links:

ISSN 0034-6861, Document, MathReview (A. Erdélyi), ZentralBlatt.

Referenced by:

§33.22(v).

Encodings:

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R. Bo and R. Wong (1994)
Uniform asymptotic expansion of Charlier polynomials,

Methods Appl. Anal. 1 (3), pp. 294–313.

External Links:

ISSN 1073-2772, Pdf, MathReview (Eberhard Wagner), ZentralBlatt.

Referenced by:

¶ ‣ §18.24.

Encodings:

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R. Bo and R. Wong (1996)
Asymptotic behavior of the Pollaczek polynomials and their zeros,

Stud. Appl. Math. 96, pp. 307–338.

External Links:

ISSN 0022-2526, MathReview (Harold Exton), ZentralBlatt.

Referenced by:

§18.35(iii).

Encodings:

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R. Bo and R. Wong (1999)
A uniform asymptotic formula for orthogonal polynomials associated with $\mathop{\exp\/}\nolimits(-x^{4})$ ,

J. Approx. Theory 98, pp. 146–166.

External Links:

ISSN 0021-9045, Document, MathReview (V. L. Deshpande), ZentralBlatt.

Referenced by:

§18.32.

Encodings:

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P. Boalch (2005)
From Klein to Painlevé via Fourier, Laplace and Jimbo,

Proc. London Math. Soc. (3) 90 (1), pp. 167–208.

External Links:

ISSN 0024-6115, Document, MathReview (Andrei A. Kapaev), ZentralBlatt.

Referenced by:

§32.9(iii).

Encodings:

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P. Boalch (2006)
The fifty-two icosahedral solutions to Painlevé VI,

J. Reine Angew. Math. 596, pp. 183–214.

External Links:

ISSN 0075-4102, Document, MathReview (Andrei A. Kapaev), ZentralBlatt.

Referenced by:

§32.9(iii).

Encodings:

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A. I. Bobenko (1991)
Constant mean curvature surfaces and integrable equations,

Uspekhi Mat. Nauk 46 (4(280)), pp. 3–42, 192 (Russian).

Notes:

In Russian. English translation: Russian Math. Surveys, 46(1991), no. 4, pp. 1–45

External Links:

ISSN 0042-1316, MathReview (P. E. Markov), ZentralBlatt.

Referenced by:

§32.11(iv).

Encodings:

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A. Bobenko and A. Its (1995)
The Painlevé III equation and the Iwasawa decomposition,

Manuscripta Math. 87 (3), pp. 369–377.

External Links:

ISSN 0025-2611, Document, MathReview (J. Dorfmeister), ZentralBlatt.

Referenced by:

§32.11(iv).

Encodings:

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S. Bochner (1952)
Bessel functions and modular relations of higher type and hyperbolic differential equations,

Comm. Sém. Math. Univ. Lund [Medd. Lunds Univ. Mat. Sem.] 1952 (Tome Supplementaire), pp. 12–20.

External Links:

MathReview (S. C. van Veen), ZentralBlatt.

Referenced by:

§35.5(i).

Encodings:

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S. Bochner and W. T. Martin (1948)
Several Complex Variables,

Princeton Mathematical Series, Vol. 10, Princeton University Press, Princeton, N. J..

External Links:

MathReview (P. Thullen), ZentralBlatt.

Referenced by:

§35.2.

Encodings:

BibTeX
A. A. Bogush and V. S. Otchik (1997)
Problem of two Coulomb centres at large intercentre separation: Asymptotic expansions from analytical solutions of the Heun equation,

J. Phys. A 30 (2), pp. 559–571.

External Links:

ISSN 0305-4470, Document, MathReview, ZentralBlatt.

Referenced by:

§31.13.

Encodings:

BibTeX
R. F. Boisvert and B. V. Saunders (1992)
Portable vectorized software for Bessel function evaluation,

ACM Trans. Math. Software 18 (4), pp. 456–469.

Notes:

Single- and double-precision Fortran, maximum accuracy 17D. For corrigendum see same journal 19(1993), p. 131

External Links:

ISSN 0098-3500, Document, Package VFNLIB (in GAMS), ZentralBlatt.

Referenced by:

§10.77(ii).

Encodings:

BibTeX
M. Born and E. Wolf (1999)
Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light,

7th edition, Cambridge University Press, Cambridge.

External Links:

ISBN 0-521-64222-1.

Referenced by:

§7.21.

Encodings:

BibTeX
J. M. Borwein and P. B. Borwein (1991)
A cubic counterpart of Jacobi’s identity and the AGM,

Trans. Amer. Math. Soc. 323 (2), pp. 691–701.

External Links:

ISSN 0002-9947, FullText, MathReview (Bruce C. Berndt), ZentralBlatt.

Referenced by:

¶ ‣ §15.8(v).

Encodings:

BibTeX
J. M. Borwein and I. J. Zucker (1992)
Fast evaluation of the gamma function for small rational fractions using complete elliptic integrals of the first kind,

IMA J. Numer. Anal. 12 (4), pp. 519–526.

External Links:

ISSN 0272-4979, MathReview, ZentralBlatt.

Referenced by:

§5.21, §5.24(ii).

Encodings:

BibTeX
J. M. Borwein and P. B. Borwein (1987)
Pi and the AGM, A Study in Analytic Number Theory and Computational Complexity,

Canadian Mathematical Society Series of Monographs and Advanced Texts, John Wiley & Sons Inc., New York.

External Links:

ISBN 0-471-83138-7, MathReview (H. London), ZentralBlatt.

Referenced by:

§19.35(i), §19.5, §19.8(i), §23.20(iv).

Encodings:

BibTeX
J. M. Borwein, D. M. Bradley and R. E. Crandall (2000)
Computational strategies for the Riemann zeta function,

J. Comput. Appl. Math. 121 (1-2), pp. 247–296.

External Links:

ISSN 0377-0427, Document, MathReview (Cem Y. Yildirim), ZentralBlatt.

Referenced by:

§27.18.

Encodings:

BibTeX
J. M. Borwein and R. M. Corless (1999)
Emerging tools for experimental mathematics,

Amer. Math. Monthly 106 (10), pp. 889–909.

External Links:

ISSN 0002-9890, MathReview (Michael M. Dediu), ZentralBlatt.

Referenced by:

§4.13.

Encodings:

BibTeX
D. L. Bosley (1996)
A technique for the numerical verification of asymptotic expansions,

SIAM Rev. 38 (1), pp. 128–135.

External Links:

ISSN 0036-1445, Document, MathReview (Yu Cheng Su), ZentralBlatt.

Referenced by:

§2.11(i).

Encodings:

BibTeX
W. Bosma and M.-P. van der Hulst (1990)
Faster Primality Testing,

(J. Vandewalle Ed.), Lecture Notes in Computer Science, Vol. 434, New York, pp. 652–656.

External Links:

ZentralBlatt.

Referenced by:

§27.18.

Encodings:

BibTeX
T. Bountis, H. Segur and F. Vivaldi (1982)
Integrable Hamiltonian systems and the Painlevé property,

Phys. Rev. A (3) 25 (3), pp. 1257–1264.

External Links:

ISSN 0556-2791, Document, MathReview.

Referenced by:

¶ ‣ §32.16.

Encodings:

BibTeX
P. Boutroux (1913)
Recherches sur les transcendantes de M. Painlevé et l’étude asymptotique des équations différentielles du second ordre,

Ann. Sci. École Norm. Sup. (3) 30, pp. 255–375.

External Links:

ISSN 0012-9593, MathReview Entry, ZentralBlatt.

Referenced by:

§32.12(i), §32.12(ii).

Encodings:

BibTeX
C. J. Bouwkamp (1947)
On spheroidal wave functions of order zero,

J. Math. Phys. Mass. Inst. Tech. 26, pp. 79–92.

External Links:

ISSN 0097-1421, MathReview (M. J. O. Strutt), ZentralBlatt.

Referenced by:

§30.16(i).

Encodings:

BibTeX
C. J. Bouwkamp (1948)
A note on Mathieu functions,

Proc. Nederl. Akad. Wetensch. 51 (7), pp. 891–893=Indagationes Math. 10, 319–321 (1948).

External Links:

MathReview (M. J. O. Strutt), ZentralBlatt.

Referenced by:

§28.7.

Encodings:

BibTeX
F. Bowman (1953)
Introduction to Elliptic Functions with Applications,

English Universities Press, Ltd., London.

Notes:

Reprinted by Dover Publications Inc., New York, 1961.

External Links:

MathReview (A. Erdélyi), ZentralBlatt.

Referenced by:

§19.30(iii), §19.32, §19.33(i), §22.15(i), §22.15(ii), §22.15(ii), §22.18(ii), §22.19(v), Ch.22.

Encodings:

BibTeX
F. Bowman (1958)
Introduction to Bessel Functions,

Dover Publications Inc., New York.

Notes:

Unaltered republication of the 1938 edition, published by Longmans, Green and Co., London-New York.

External Links:

MathReview, ZentralBlatt.

Referenced by:

§10.73(iii).

Encodings:

BibTeX
K. O. Bowman (1984)
Computation of the polygamma functions,

Comm. Statist. B—Simulation Comput. 13 (3), pp. 409–415.

External Links:

ISSN 0361-0918, Document, MathReview (S. Conde).

Referenced by:

§5.24(iii).

Encodings:

BibTeX
J. P. Boyd and A. Natarov (1998)
A Sturm-Liouville eigenproblem of the fourth kind: A critical latitude with equatorial trapping,

Stud. Appl. Math. 101 (4), pp. 433–455.

External Links:

ISSN 0022-2526, Document, MathReview, ZentralBlatt.

Referenced by:

§31.17(ii).

Encodings:

BibTeX
J. P. Boyd (1998)
Weakly Nonlocal Solitary Waves and Beyond-All-Orders Asymptotics,

Mathematics and its Applications, Vol. 442, Kluwer Academic Publishers, Boston-Dordrecht.

External Links:

ISBN 0-7923-5072-3, MathReview (Alan Jeffrey), ZentralBlatt.

Referenced by:

§22.19(iii).

Encodings:

BibTeX
W. G. C. Boyd and T. M. Dunster (1986)
Uniform asymptotic solutions of a class of second-order linear differential equations having a turning point and a regular singularity, with an application to Legendre functions,

SIAM J. Math. Anal. 17 (2), pp. 422–450.

External Links:

ISSN 0036-1410, Document, MathReview (F. W. J. Olver), ZentralBlatt.

Referenced by:

§14.15(iv), §14.15(iv), §14.26, §2.8(vi).

Encodings:

BibTeX
W. G. C. Boyd (1973)
The asymptotic analysis of canonical problems in high-frequency scattering theory. II. The circular and parabolic cylinders,

Proc. Cambridge Philos. Soc. 74, pp. 313–332.

External Links:

Document, MathReview (Y. M. Chen).

Referenced by:

§12.17.

Encodings:

BibTeX
W. G. C. Boyd (1987)
Asymptotic expansions for the coefficient functions that arise in turning-point problems,

Proc. Roy. Soc. London Ser. A 410, pp. 35–60.

External Links:

ISSN 0080-4630, FullText, MathReview (P. F. Hsieh), ZentralBlatt.

Referenced by:

§2.8(iii).

Encodings:

BibTeX
W. G. C. Boyd (1990a)
Asymptotic Expansions for the Coefficient Functions Associated with Linear Second-order Differential Equations: The Simple Pole Case,

in Asymptotic and Computational Analysis (Winnipeg, MB, 1989),

Lecture Notes in Pure and Applied Mathematics, Vol. 124, pp. 53–73.

External Links:

MathReview (John S. Lew), ZentralBlatt.

Referenced by:

§2.8(iv).

Encodings:

BibTeX
W. G. C. Boyd (1990b)
Stieltjes transforms and the Stokes phenomenon,

Proc. Roy. Soc. London Ser. A 429, pp. 227–246.

External Links:

ISSN 0962-8444, FullText, MathReview, ZentralBlatt.

Referenced by:

§2.11(v).

Encodings:

BibTeX
W. G. C. Boyd (1993)
Error bounds for the method of steepest descents,

Proc. Roy. Soc. London Ser. A 440, pp. 493–518.

External Links:

ISSN 0962-8444, FullText, MathReview (Pablo Martín), ZentralBlatt.

Referenced by:

§2.3(iii), §2.4(iii), §9.10(ii), §9.7(iv).

Encodings:

BibTeX
W. G. C. Boyd (1994)
Gamma function asymptotics by an extension of the method of steepest descents,

Proc. Roy. Soc. London Ser. A 447, pp. 609–630.

External Links:

ISSN 0962-8444, FullText, MathReview (Jens Bolte), ZentralBlatt.

Referenced by:

§5.11(i), §5.11(ii), §5.11(ii).

Encodings:

BibTeX
W. G. C. Boyd (1995)
Approximations for the late coefficients in asymptotic expansions arising in the method of steepest descents,

Methods Appl. Anal. 2 (4), pp. 475–489.

External Links:

ISSN 1073-2772, Pdf, MathReview (Dan Polis̆evski), ZentralBlatt.

Referenced by:

§2.4(iv).

Encodings:

BibTeX
T. H. Boyer (1969)
Concerning the zeros of some functions related to Bessel functions,

J. Mathematical Phys. 10 (9), pp. 1729–1744.

External Links:

Document, MathReview (C. V. Coffman), ZentralBlatt.

Referenced by:

§10.21(xi).

Encodings:

BibTeX
B. L. J. Braaksma and B. Meulenbeld (1967)
Integral transforms with generalized Legendre functions as kernels,

Compositio Math. 18, pp. 235–287.

External Links:

MathReview (R. K. Saxena), ZentralBlatt.

Referenced by:

§14.20(vi), §14.29, §14.31(ii).

Encodings:

BibTeX
M. Brack, M. Mehta and K. Tanaka (2001)
Occurrence of periodic Lamé functions at bifurcations in chaotic Hamiltonian systems,

J. Phys. A 34 (40), pp. 8199–8220.

External Links:

ISSN 0305-4470, Document, MathReview, ZentralBlatt.

Referenced by:

§29.19(i).

Encodings:

BibTeX
W. J. Braithwaite (1973)
Associated Legendre polynomials, ordinary and modified spherical harmonics,

Comput. Phys. Comm. 5 (5), pp. 390–394.

Notes:

Single-precision Fortran, maximum accuracy 16S

External Links:

Document, Code.

Referenced by:

§14.34(ii).

Encodings:

BibTeX
N. Brazel, F. Lawless and A. Wood (1992)
Exponential asymptotics for an eigenvalue of a problem involving parabolic cylinder functions,

Proc. Amer. Math. Soc. 114 (4), pp. 1025–1032.

External Links:

ISSN 0002-9939, FullText, MathReview, ZentralBlatt.

Referenced by:

§12.16.

Encodings:

BibTeX
R. P. Brent (1978a)
A Fortran multiple-precision arithmetic package,

ACM Trans. Math. Software 4 (1), pp. 57–70.

External Links:

ISSN 0098-3500, Document.

Referenced by:

§4.48(iii).

Encodings:

BibTeX
R. P. Brent (1976)
Fast multiple-precision evaluation of elementary functions,

J. Assoc. Comput. Mach. 23 (2), pp. 242–251.

External Links:

Document, MathReview (Amnon Barak), ZentralBlatt.

Referenced by:

¶ ‣ §4.45(i).

Encodings:

BibTeX
R. P. Brent (1978b)
Algorithm 524: MP, A Fortran multiple-precision arithmetic package [A1],

ACM Trans. Math. Software 4 (1), pp. 71–81.

External Links:

ISSN 0098-3500, Document, Remark. TOMS module 524 (in GAMS).

Referenced by:

§10.77(iii), §24.21(ii), §25.21(ii), §25.21(v), §5.24(ii), §7.25(ii), §7.25(vi).

Encodings:

BibTeX
D. M. Bressoud (1989)
Factorization and Primality Testing,

Springer-Verlag, New York.

External Links:

ISBN 0-387-97040-1, MathReview (Brigitte Vallée), ZentralBlatt.

Referenced by:

§23.20(iii), §27.19, David M. Bressoud.

Encodings:

BibTeX
D. M. Bressoud (1999)
Proofs and Confirmations: The Story of the Alternating Sign Matrix Conjecture,

Cambridge University Press, Cambridge.

External Links:

ISBN 0-521-66170-6; 0-521-66646-5, MathReview (George E. Andrews), ZentralBlatt.

Referenced by:

§1.3(ii), §26.10(ii), §26.10(iii), §26.12(i), §26.12(ii), §26.12(iii), §26.19, §26.20, §26.9(iii), David M. Bressoud.

Encodings:

BibTeX
D. Bressoud and S. Wagon (2000)
A Course in Computational Number Theory,

Key College Publishing, Emeryville, CA.

Notes:

With 1 CD-ROM (Windows, Macintosh and UNIX) containing a collection of Mathematica programs for computations in number theory.

External Links:

ISBN 1-930190-10-7, MathReview (Samuel S. Wagstaff, Jr.), ZentralBlatt.

Referenced by:

¶ ‣ §27.12, §27.19, §27.21, §27.22, David M. Bressoud.

Encodings:

BibTeX
C. Brezinski (1999)
Error estimates for the solution of linear systems,

SIAM J. Sci. Comput. 21 (2), pp. 764–781.

External Links:

ISSN 1095-7197, Document, MathReview (Dimitrios Noutsos), ZentralBlatt.

Referenced by:

§3.2(iii).

Encodings:

BibTeX
C. Brezinski and M. Redivo Zaglia (1991)
Extrapolation Methods. Theory and Practice,

Studies in Computational Mathematics, Vol. 2, North-Holland Publishing Co., Amsterdam.

Notes:

With 1 IBM-PC floppy disk (5.25 inch)

External Links:

ISBN 0-444-88814-4, MathReview (Alan M. Cohen), ZentralBlatt.

Referenced by:

§3.9(iii), §3.9(iv), §3.9(v), §3.9(vi).

Encodings:

BibTeX
C. Brezinski (1980)
Padé-type Approximation and General Orthogonal Polynomials,

International Series of Numerical Mathematics, Vol. 50, Birkhäuser Verlag, Basel.

External Links:

ISBN 3-7643-1100-2, MathReview (A. Magnus), ZentralBlatt.

Referenced by:

¶ ‣ §3.11(iv).

Encodings:

BibTeX
E. Brieskorn and H. Knörrer (1986)
Plane Algebraic Curves,

Birkhäuser Verlag, Basel.

Notes:

Translated from the German by John Stillwell

External Links:

ISBN 3-7643-1769-8, MathReview, ZentralBlatt.

Referenced by:

§21.7(i).

Encodings:

BibTeX
J. Brillhart (1969)
On the Euler and Bernoulli polynomials,

J. Reine Angew. Math. 234, pp. 45–64.

External Links:

ISSN 0075-4102, MathReview (L. Carlitz), ZentralBlatt.

Referenced by:

§24.12(iv).

Encodings:

BibTeX
D. M. Brink and G. R. Satchler (1993)
Angular Momentum,

3rd edition, Oxford University Press, Oxford.

External Links:

ISBN 0-19-851759-9.

Referenced by:

§34.9.

Encodings:

BibTeX
British Association for the Advancement of Science (1937)
Bessel Functions. Part I: Functions of Orders Zero and Unity,

Mathematical Tables, Volume 6, Cambridge University Press, Cambridge.

External Links:

ISBN 0-521-04319-0, ZentralBlatt.

Referenced by:

§10.1, §10.75(ii), ¶ ‣ §10.75(iii), §10.75(v).

Encodings:

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J. C. Bronski, L. D. Carr, B. Deconinck, J. N. Kutz and K. Promislow (2001)
Stability of repulsive Bose-Einstein condensates in a periodic potential,

Phys. Rev. E (3) 63 (036612), pp. 1–11.

External Links:

Document.

Referenced by:

§29.19(i).

Encodings:

BibTeX
Yu. A. Brychkov and K. O. Geddes (2005)
On the derivatives of the Bessel and Struve functions with respect to the order,

Integral Transforms Spec. Funct. 16 (3), pp. 187–198.

External Links:

ISSN 1065-2469, Document, MathReview (Boro Döring), ZentralBlatt.

Referenced by:

¶ ‣ §10.15, ¶ ‣ §10.38, §11.4(vi).

Encodings:

BibTeX
E. Brézin, C. Itzykson, G. Parisi and J. B. Zuber (1978)
Planar diagrams,

Comm. Math. Phys. 59 (1), pp. 35–51.

External Links:

ISSN 0010-3616, Document, MathReview (C. S. Sharma), ZentralBlatt.

Referenced by:

§32.15.

Encodings:

BibTeX
J. Brüning (1984)
On the asymptotic expansion of some integrals,

Arch. Math. (Basel) 42 (3), pp. 253–259.

External Links:

ISSN 0003-889X, Document, MathReview (E. Riekstiņš), ZentralBlatt.

Referenced by:

§2.5(ii).

Encodings:

BibTeX
H. Buchholz (1969)
The Confluent Hypergeometric Function with Special Emphasis on Its Applications,

Springer-Verlag, New York.

Notes:

Translated from the German by H. Lichtbau and K. Wetzel

External Links:

MathReview, ZentralBlatt.

Referenced by:

§12.17, §12.17, Ch.12, §13.1, §13.10(v), §13.14(i), §13.16(ii), §13.16(iii), §13.23(i), §13.24, §13.4(i), §13.4(ii), §13.4(iii), §13.6(iv), §13.9(i), §13.9(ii), Ch.13, §33.6.

Encodings:

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J. D. Buckholtz (1963)
Concerning an approximation of Copson,

Proc. Amer. Math. Soc. 14 (4), pp. 564–568.

External Links:

FullText, MathReview (L. Carlitz), ZentralBlatt.

Referenced by:

§8.11(v).

Encodings:

BibTeX
J. P. Buhler, R. E. Crandall and R. W. Sompolski (1992)
Irregular primes to one million,

Math. Comp. 59 (200), pp. 717–722.

External Links:

ISSN 0025-5718, FullText, MathReview (Duncan A. Buell), ZentralBlatt.

Referenced by:

§24.19(ii).

Encodings:

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J. Buhler, R. Crandall, R. Ernvall, T. Metsänkylä and M. A. Shokrollahi (2001)
Irregular primes and cyclotomic invariants to 12 million,

J. Symbolic Comput. 31 (1-2), pp. 89–96.

Notes:

Computational algebra and number theory (Milwaukee, WI, 1996)

External Links:

ISSN 0747-7171, Document, MathReview (Xavier-François Roblot), ZentralBlatt.

Referenced by:

§24.19(ii).

Encodings:

BibTeX
R. Bulirsch (1969a)
An extension of the Bartky-transformation to incomplete elliptic integrals of the third kind,

Numer. Math. 13 (3), pp. 266–284.

External Links:

ISSN 0029-599X, Document, MathReview (Y. L. Luke), ZentralBlatt.

Referenced by:

§19.1, §19.2(iii), ¶ ‣ §19.36(ii), ¶ ‣ §19.36(ii).

Encodings:

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R. Bulirsch (1969b)
Numerical calculation of elliptic integrals and elliptic functions. III,

Numer. Math. 13 (4), pp. 305–315.

Notes:

Algol 60 programs for the incomplete elliptic integral of the third kind, and for a general complete elliptic integral, are included.

External Links:

ISSN 0029-599X, Document, MathReview, ZentralBlatt.

Referenced by:

§19.2(iii), ¶ ‣ §19.36(ii), ¶ ‣ §19.36(ii), §19.39(ii), §19.39(iii), R. Bulirsch (1965a).

Encodings:

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R. Bulirsch and H. Rutishauser (1968)
Interpolation und genäherte Quadratur,

in Mathematische Hilfsmittel des Ingenieurs. Teil III,

(I. Szabó Ed.), Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen, Vol. 141, pp. 232–319.

External Links:

MathReview (E. Kreyszig).

Referenced by:

§3.3(vi).

Encodings:

BibTeX
R. Bulirsch and J. Stoer (1968)
II. Darstellung von Funktionen in Rechenautomaten,

in Mathematische Hilfsmittel des Ingenieurs. Teil III,

(I. Szabó Ed.).

External Links:

MathReview (E. Kreyszig).

Referenced by:

§19.2(iii), ¶ ‣ §19.36(ii).

Encodings:

BibTeX
R. Bulirsch (1965a)
Numerical calculation of elliptic integrals and elliptic functions. II,

Numer. Math. 7 (4), pp. 353–354.

Notes:

An improved Algol 60 program for the complete elliptic integral of the third kind is included, but superseded by a program in Bulirsch (1969b).

External Links:

ISSN 0029-599X, Document, MathReview (M. P. S. Madan), ZentralBlatt.

Referenced by:

§19.1.

Encodings:

BibTeX
R. Bulirsch (1965b)
Numerical calculation of elliptic integrals and elliptic functions,

Numer. Math. 7 (1), pp. 78–90.

Notes:

Algol 60 programs are included for real and complex elliptic integrals, and for Jacobian elliptic functions of real argument.

External Links:

ISSN 0029-599X, Document, MathReview (M. Feliciano), ZentralBlatt.

Referenced by:

§19.1, §19.2(iii), ¶ ‣ §19.36(ii), §19.39(iii), §22.22(ii).

Encodings:

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R. Bulirsch (1967)
Numerical calculation of the sine, cosine and Fresnel integrals,

Numer. Math. 9 (5), pp. 380–385.

Notes:

Algol 60 procedures for sine, cosine, and 2 Fresnel integrals are included.

External Links:

ISSN 0029-599X, ISSN 0029-599X, Document, MathReview Entry.

Referenced by:

§7.24(ii), §7.25(iv).

Encodings:

BibTeX
P. S. Bullen (1998)
A Dictionary of Inequalities,

Pitman Monographs and Surveys in Pure and Applied Mathematics, Vol. 97, Longman, Harlow.

External Links:

ISBN 0-8493-0634-5, MathReview (Lucio Renato Berrone), ZentralBlatt.

Referenced by:

¶ ‣ §4.18, §4.5(i), §4.5(ii).

Encodings:

BibTeX
J. L. Burchnall and T. W. Chaundy (1940)
Expansions of Appell’s double hypergeometric functions,

Quart. J. Math., Oxford Ser. 11, pp. 249–270.

External Links:

Document, MathReview (G. Szegö), ZentralBlatt.

Referenced by:

§15.16, §16.16(i).

Encodings:

BibTeX
J. L. Burchnall and T. W. Chaundy (1941)
Expansions of Appell’s double hypergeometric functions. II,

Quart. J. Math., Oxford Ser. 12, pp. 112–128.

External Links:

Document, MathReview (G. Szegö), ZentralBlatt.

Referenced by:

§16.16(i).

Encodings:

BibTeX
J. L. Burchnall and T. W. Chaundy (1948)
The hypergeometric identities of Cayley, Orr, and Bailey,

Proc. London Math. Soc. (2) 50, pp. 56–74.

External Links:

Document, MathReview (N. A. Hall), ZentralBlatt.

Referenced by:

§15.16.

Encodings:

BibTeX
A. Burgess (1963)
The determination of phases and amplitudes of wave functions,

Proc. Phys. Soc. 81 (3), pp. 442–452.

External Links:

Document.

Referenced by:

§33.23(vii).

Encodings:

BibTeX
P. G. Burke (1970)
A program to calculate a general recoupling coefficient,

Comput. Phys. Comm. 1 (4), pp. 241–250.

Notes:

Single-precision Fortran

External Links:

Document, Code.

Referenced by:

§34.15.

Encodings:

BibTeX
T. W. Burkhardt and T. Xue (1991)
Density profiles in confined critical systems and conformal invariance,

Phys. Rev. Lett. 66 (7), pp. 895–898.

External Links:

Document.

Referenced by:

§15.18.

Encodings:

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W. S. Burnside and A. W. Panton (1960)
The Theory of Equations: With an Introduction to the Theory of Binary Algebraic Forms,

Dover Publications, New York.

Notes:

Two volumes. A reproduction of the seventh edition [vol. 1, Longmans, Green, London 1912; vol. 2, Longmans, Green, London 1928].

External Links:

MathReview, ZentralBlatt.

Referenced by:

§1.11(i), §1.11(ii), §1.11(iv).

Encodings:

BibTeX
K. H. Burrell (1974)
Algorithm 484: Evaluation of the modified Bessel functions K0(Z) and K1(Z) for complex arguments,

Comm. ACM 17 (9), pp. 524–526.

Notes:

Double-precision Fortran code, maximum accuracy 13S.

External Links:

ISSN 0001-0782, Document, Code.

Referenced by:

§10.77(iv).

Encodings:

BibTeX
A. I. Burshtein and S. I. Temkin (1994)
Spectroscopy of Molecular Rotation in Gases and Liquids,

Cambridge University Press, Cambridge.

External Links:

ISBN 0-521-45465-4.

Referenced by:

§34.12.

Encodings:

BibTeX
N. M. Burunova (1960)
A Guide to Mathematical Tables: Supplement No. 1,

Pergamon Press, New York.

Notes:

Supplement to “A Guide to Mathematical Tables” by A. V. Lebedev and R. M. Fedorova.

External Links:

MathReview.

Referenced by:

A. V. Lebedev and R. M. Fedorova (1960).

Encodings:

BibTeX
T. Busch, B. Englert, K. Rzażewski and M. Wilkens (1998)
Two cold atoms in a harmonic trap,

Found. Phys. 28 (4), pp. 549–559.

External Links:

Document.

Referenced by:

§12.17.

Encodings:

BibTeX
P. J. Bushell (1987)
On a generalization of Barton’s integral and related integrals of complete elliptic integrals,

Math. Proc. Cambridge Philos. Soc. 101 (1), pp. 1–5.

External Links:

ISSN 0305-0041, MathReview (J. M. H. Peters), ZentralBlatt.

Referenced by:

§19.13(i).

Encodings:

BibTeX
J. C. Butcher (1987)
The Numerical Analysis of Ordinary Differential Equations. Runge-Kutta and General Linear Methods,

John Wiley & Sons Ltd., Chichester.

External Links:

ISBN 0-471-91046-5, MathReview (Peter Alfeld), ZentralBlatt.

Referenced by:

¶ ‣ §3.7(v).

Encodings:

BibTeX
J. C. Butcher (2003)
Numerical Methods for Ordinary Differential Equations,

John Wiley & Sons Ltd., Chichester.

External Links:

ISBN 0-471-96758-0, MathReview (Ian Gladwell), ZentralBlatt.

Referenced by:

§32.17.

Encodings:

BibTeX
R. W. Butler and A. T. A. Wood (2002)
Laplace approximations for hypergeometric functions with matrix argument,

Ann. Statist. 30 (4), pp. 1155–1177.

External Links:

ISSN 0090-5364, Document, MathReview, ZentralBlatt.

Referenced by:

§35.6(iv), §35.7(iv), §35.7(iv), §35.9.

Encodings:

BibTeX
R. W. Butler and A. T. A. Wood (2003)
Laplace approximation for Bessel functions of matrix argument,

J. Comput. Appl. Math. 155 (2), pp. 359–382.

External Links:

ISSN 0377-0427, Document, MathReview (S. Bhargava), ZentralBlatt.

Referenced by:

§35.5(ii), §35.5(iii).

Encodings:

BibTeX
P. L. Butzer, M. Hauss and M. Leclerc (1992)
Bernoulli numbers and polynomials of arbitrary complex indices,

Appl. Math. Lett. 5 (6), pp. 83–88.

External Links:

ISSN 0893-9659, MathReview, ZentralBlatt.

Referenced by:

§24.16(iii).

Encodings:

BibTeX
P. L. Butzer and M. Hauss (1992)
Riemann zeta function: Rapidly converging series and integral representations,

Appl. Math. Lett. 5 (2), pp. 83–88.

External Links:

ISSN 0893-9659, Document, MathReview (Jacek Fabrykowski), ZentralBlatt.

Referenced by:

§25.18(i).

Encodings:

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P. L. Butzer, S. Flocke and M. Hauss (1994)
Euler functions ${E}_{\alpha}(z)$ with complex $\alpha$ and applications,

in Approximation, probability, and related fields (Santa Barbara, CA, 1993),

(S. T. Rachev Ed.), pp. 127–150.

External Links:

MathReview (R. N. Kalia), ZentralBlatt.

Referenced by:

§24.16(iii).

Encodings:

BibTeX
B. L. Buzbee (1984)
The SLATEC Common Mathematical Library,

in Sources and Development of Mathematical Software,

pp. 302–320.

External Links:

Package SLATEC (in GAMS).

Referenced by:

SLATEC (free Fortran library).

Encodings:

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J. G. Byatt-Smith (2000)
The Borel transform and its use in the summation of asymptotic expansions,

Stud. Appl. Math. 105 (2), pp. 83–113.

External Links:

ISSN 0022-2526, Document, MathReview (A. D. Wood), ZentralBlatt.

Referenced by:

§2.11(v).

Encodings:

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W. E. Byerly (1888)
Elements of the Integral Calculus,

2nd edition, Ginn & Co., Boston.

Notes:

Reprinted by G. E. Stechert, New York, 1926

Referenced by:

§19.11(i), Ch.19.

Encodings:

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P. F. Byrd and M. D. Friedman (1971)
Handbook of Elliptic Integrals for Engineers and Scientists,

2nd edition, Die Grundlehren der mathematischen Wissenschaften, Band 67, Springer-Verlag, New York.

Notes:

Table errata: Math. Comp. v. 66 (1997), no. 220, p. 1767, v. 36 (1981), no. 153, p. 317,319, v. 26 (1972), no. 118, p. 597.

External Links:

MathReview, ZentralBlatt.

Referenced by:

§19.1, §19.13(i), §19.13(i), §19.13(ii), §19.14(ii), §19.29(i), §19.30(ii), ¶ ‣ §19.37(ii), ¶ ‣ §19.37(ii), ¶ ‣ §19.37(ii), ¶ ‣ §19.37(ii), ¶ ‣ §19.37(iii), §19.4(ii), §19.4(ii), §19.5, §19.6(i), §19.6(iv), Ch.19, §22.11.

Encodings:

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W. Börsch-Supan (1960)
Algorithm 21: Bessel function for a set of integer orders,

Comm. ACM 3 (11), pp. 600.

Notes:

Includes Algol code, minimum accuracy 5S. For certification see same journal 8(1965), p. 219.

External Links:

ISSN 0001-0782, Document.

Referenced by:

§10.77(ii).

Encodings:

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W. Bühring (1987a)
An analytic continuation of the hypergeometric series,

SIAM J. Math. Anal. 18 (3), pp. 884–889.

External Links:

ISSN 0036-1410, Document, MathReview (H. M. Srivastava), ZentralBlatt.

Referenced by:

§15.15, §15.19(i).

Encodings:

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W. Bühring (1987b)
The behavior at unit argument of the hypergeometric function $\mathop{{{}_{{3}}F_{{2}}}\/}\nolimits$ ,

SIAM J. Math. Anal. 18 (5), pp. 1227–1234.

External Links:

ISSN 0036-1410, Document, MathReview (K. M. Saksena), ZentralBlatt.

Referenced by:

§16.8(ii).

Encodings:

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W. Bühring (1988)
An analytic continuation formula for the generalized hypergeometric function,

SIAM J. Math. Anal. 19 (5), pp. 1249–1251.

External Links:

ISSN 0036-1410, Document, MathReview (H. M. Srivastava), ZentralBlatt.

Referenced by:

§16.8(ii).

Encodings:

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W. Bühring (1992)
Generalized hypergeometric functions at unit argument,

Proc. Amer. Math. Soc. 114 (1), pp. 145–153.

External Links:

ISSN 0002-9939, FullText, MathReview (R. K. Raina), ZentralBlatt.

Referenced by:

§16.4(ii), §16.8(ii).

Encodings:

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W. Bühring (1994)
The double confluent Heun equation: Characteristic exponent and connection formulae,

Methods Appl. Anal. 1 (3), pp. 348–370.

External Links:

ISSN 1073-2772, FullText, MathReview (W. Balser), ZentralBlatt.

Referenced by:

¶ ‣ §31.12.

Encodings:

BibTeX