Bibliography M

♦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♦

H. Maass (1971)
Siegel’s modular forms and Dirichlet series,

Lecture Notes in Mathematics, Vol. 216, Springer-Verlag, Berlin.

External Links:

Document, MathReview (K.-B. Gundlach), ZentralBlatt.

Referenced by:

§35.4(ii).

Encodings:

BibTeX
D. A. MacDonald (1989)
The roots of $\mathop{J_{{0}}\/}\nolimits\!\left(z\right)-i\mathop{J_{{1}}\/}\nolimits\!\left(z\right)=0$ ,

Quart. Appl. Math. 47 (2), pp. 375–378.

External Links:

ISSN 0033-569X, MathReview, ZentralBlatt.

Referenced by:

¶ ‣ §10.21(ix), ¶ ‣ §10.75(iii).

Encodings:

BibTeX
D. A. MacDonald (1997)
On the computation of zeroes of $J_{n}(z)-iJ_{{n+1}}(z)=0$ ,

Quart. Appl. Math. 55 (4), pp. 623–633.

External Links:

ISSN 0033-569X, MathReview (Andrea Laforgia), ZentralBlatt.

Referenced by:

¶ ‣ §10.21(ix).

Encodings:

BibTeX
I. G. Macdonald (1972)
Affine root systems and Dedekind’s $\eta$ -function,

Invent. Math. 15 (2), pp. 91–143.

External Links:

Document, MathReview (D.-N. Verma), ZentralBlatt.

Referenced by:

§20.12(i).

Encodings:

BibTeX
I. G. Macdonald (1982)
Some conjectures for root systems,

SIAM J. Math. Anal. 13 (6), pp. 988–1007.

External Links:

ISSN 0036-1410, Document, MathReview (S. Milne), ZentralBlatt.

Referenced by:

¶ ‣ §17.13, ¶ ‣ §17.14.

Encodings:

BibTeX
I. G. Macdonald (1990)
Hypergeometric Functions,

Notes:

Unpublished Lecture Notes, University of London. An online version exists.

External Links:

FullText.

Referenced by:

§35.7(ii), §35.8(iii).

Encodings:

BibTeX
I. G. Macdonald (1995)
Symmetric Functions and Hall Polynomials,

2nd edition, The Clarendon Press, Oxford University Press, New York-Oxford.

Notes:

With contributions by A. Zelevinsky. Paperback version published by Oxford University Press, July 1999.

External Links:

ISBN 0-19-853489-2; 0-19-850450-0, MathReview (John R. Stembridge), ZentralBlatt.

Referenced by:

§18.37(iii), §26.19, §35.4(i), §35.4(ii).

Encodings:

BibTeX
I. G. Macdonald (1998)
Symmetric Functions and Orthogonal Polynomials,

University Lecture Series, Vol. 12, American Mathematical Society, Providence, RI.

External Links:

ISBN 0-8218-0770-6, MathReview (Angèle M. Hamel), ZentralBlatt.

Referenced by:

¶ ‣ §17.14.

Encodings:

BibTeX
I. G. Macdonald (2000)
Orthogonal polynomials associated with root systems,

Sém. Lothar. Combin. 45, pp. Art. B45a, 40 pp. (electronic).

External Links:

ISSN 1286-4889, FullText, MathReview, ZentralBlatt.

Referenced by:

§18.37(iii).

Encodings:

BibTeX
I. G. Macdonald (2003)
Affine Hecke Algebras and Orthogonal Polynomials,

Cambridge Tracts in Mathematics, Vol. 157, Cambridge University Press, Cambridge.

External Links:

ISBN 0-521-82472-9, MathReview (Eric M. Opdam), ZentralBlatt.

Referenced by:

§18.37(iii).

Encodings:

BibTeX
I. D. Macdonald (1968)
The Theory of Groups,

Clarendon Press, Oxford.

Notes:

Reprinted in 1988 by Krieger Publishing Co., Malabar, FL

External Links:

ISBN 0-19-853137-0;0-89464-287-1, MathReview (A. P. Street), ZentralBlatt.

Referenced by:

§23.20(ii).

Encodings:

BibTeX
R. L. Mace and M. A. Hellberg (1995)
A dispersion function for plasmas containing superthermal particles,

Physics of Plasmas 2 (6), pp. 2098–2109.

External Links:

Document.

Referenced by:

§15.18.

Encodings:

BibTeX
N. W. Macfadyen and P. Winternitz (1971)
Crossing symmetric expansions of physical scattering amplitudes: The $O(2,1)$ group and Lamé functions,

J. Mathematical Phys. 12, pp. 281–293.

External Links:

Document, MathReview.

Referenced by:

§29.19(ii).

Encodings:

BibTeX
A. J. MacLeod (1989)
Algorithm AS 245. A robust and reliable algorithm for the logarithm of the gamma function,

Appl. Statist. 38 (2), pp. 397–402.

External Links:

FullText, Code, ZentralBlatt.

Referenced by:

§5.24(ii).

Encodings:

BibTeX
A. J. MacLeod (1993)
Chebyshev expansions for modified Struve and related functions,

Math. Comp. 60 (202), pp. 735–747.

External Links:

ISSN 0025-5718, FullText, MathReview, ZentralBlatt.

Referenced by:

§11.15(i).

Encodings:

BibTeX
A. J. MacLeod (1994)
Computation of inhomogeneous Airy functions,

J. Comput. Appl. Math. 53 (1), pp. 109–116.

External Links:

ISSN 0377-0427, Document, MathReview (Dumitru Acu), ZentralBlatt.

Referenced by:

§9.19(iv).

Encodings:

BibTeX
A. J. MacLeod (1996a)
Algorithm 757: MISCFUN, a software package to compute uncommon special functions,

ACM Trans. Math. Software 22 (3), pp. 288–301.

Notes:

Double-precision Fortran, maximum accuracy 20D.

External Links:

ISSN 0098-3500, Document, TOMS module 757 (in GAMS), MathReview Entry, ZentralBlatt.

Referenced by:

§10.77(ix), §11.16(ii), §25.21(vi), §25.21(vii), §7.25(vi), §9.20(ii), §9.20(vi).

Encodings:

BibTeX
A. J. MacLeod (1996b)
Rational approximations, software and test methods for sine and cosine integrals,

Numer. Algorithms 12 (3-4), pp. 259–272.

Notes:

Includes Fortran code, maximum accuracy 20S.

External Links:

ISSN 1017-1398, Document, MathReview, ZentralBlatt.

Referenced by:

§6.13, §6.20(i), §6.21(ii).

Encodings:

BibTeX
A. J. MacLeod (1998)
Algorithm 779: Fermi-Dirac functions of order $-1/2$ , $1/2$ , $3/2$ , $5/2$ ,

ACM Trans. Math. Software 24 (1), pp. 1–12.

Notes:

Double-precision Fortran, maximum accuracy 16D.

External Links:

ISSN 0098-3500, Document, TOMS module 779 (in GAMS), ZentralBlatt.

Referenced by:

§25.21(vii).

Encodings:

BibTeX
A. J. MacLeod (2002a)
Asymptotic expansions for the zeros of certain special functions,

J. Comput. Appl. Math. 145 (2), pp. 261–267.

External Links:

ISSN 0377-0427, Document, MathReview (Andrea Laforgia), ZentralBlatt.

Referenced by:

§10.70, §11.4(vii), §6.13.

Encodings:

BibTeX
A. J. MacLeod (2002b)
The efficient computation of some generalised exponential integrals,

J. Comput. Appl. Math. 148 (2), pp. 363–374.

External Links:

ISSN 0377-0427, Document, MathReview, ZentralBlatt.

Referenced by:

¶ ‣ §8.19(v).

Encodings:

BibTeX
T. M. MacRobert (1967)
Spherical Harmonics. An Elementary Treatise on Harmonic Functions with Applications,

3rd edition, International Series of Monographs in Pure and Applied Mathematics, Vol. 98, Pergamon Press, Oxford.

External Links:

MathReview (A. Erdélyi), ZentralBlatt.

Referenced by:

Ch.14.

Encodings:

BibTeX
Magma (Web Site)
Computational Algebra Group, School of Mathematics and Statistics, University of Sydney, Australia..

Notes:

A software package (the successor to CAYLEY) designed to solve computationally hard problems in algebra, number theory, geometry, and combinatorics, and to provide a mathematically rigorous environment for computing with algebraic, number-theoretic, combinatoric, and geometric objects.

External Links:

Magma.

Referenced by:

§26.22.

Encodings:

BibTeX
A. P. Magnus (1995)
Painlevé-type differential equations for the recurrence coefficients of semi-classical orthogonal polynomials,

J. Comput. Appl. Math. 57 (1-2), pp. 215–237.

External Links:

ISSN 0377-0427, Document, MathReview (Leonid B. Golinskiĭ), ZentralBlatt.

Referenced by:

§32.15.

Encodings:

BibTeX
W. Magnus, F. Oberhettinger and R. P. Soni (1966)
Formulas and Theorems for the Special Functions of Mathematical Physics,

3rd edition, Springer-Verlag, New York-Berlin.

Notes:

Table errata: Math. Comp. v. 23 (1969), p. 471, v. 24 (1970), pp. 240 and 505, v. 25 (1971), no. 113, p. 201, v. 29 (1975), no. 130, p. 672, v. 30 (1976), no. 135, pp. 677–678, v. 32 (1978), no. 141, pp. 319–320, v. 36 (1981), no. 153, pp. 315–317, v. 41 (1983), no. 164, pp. 775–776, and v. 81 (2012), no. 280, p. 2251

External Links:

MathReview (Mary L. Boas), ZentralBlatt.

Referenced by:

§10.15, §10.22(vi), §10.32(iv), §10.38, §10.43(vi), §10.60(iv), §10.9(iv), §11.5(iii), Ch.11, ¶ ‣ §12.12, §12.5(iv), Ch.12, §13.10(vi), §13.23(iv), §14.1, §14.11, ¶ ‣ §14.12(ii), §14.18(iv), §14.25, §14.3(iii), §14.5(v), §14.7(iv), Ch.14, §8.1.

Encodings:

BibTeX
W. Magnus and S. Winkler (1966)
Hill’s Equation,

Interscience Tracts in Pure and Applied Mathematics, No. 20, Interscience Publishers John Wiley & Sons, New York-London-Sydney.

Notes:

Reprinted by Dover Publications, Inc., New York, 1979.

External Links:

MathReview (H. Hochstadt), ZentralBlatt.

Referenced by:

§1.3(iii), §28.29(i), §28.29(ii), §28.29(ii), §28.29(iii), §28.29(iii), §28.29(iii), §28.30(i), Ch.28, §29.3(i), §29.9.

Encodings:

BibTeX
W. Magnus (1941)
Zur Theorie des zylindrisch-parabolischen Spiegels,

Z. Physik 118, pp. 343–356 (German).

External Links:

MathReview (A. Erdélyi), ZentralBlatt.

Referenced by:

§12.17.

Encodings:

BibTeX
K. Mahler (1930)
Über die Nullstellen der unvollständigen Gammafunktionen,

Rend. del Circ. Matem. Palermo 54, pp. 1–41.

External Links:

Document, ZentralBlatt.

Referenced by:

§8.11(iii).

Encodings:

BibTeX
R. S. Maier (2005)
On reducing the Heun equation to the hypergeometric equation,

J. Differential Equations 213 (1), pp. 171–203.

External Links:

ISSN 0022-0396, Document, MathReview (Wolfgang Bühring), ZentralBlatt.

Referenced by:

§31.7(i).

Encodings:

BibTeX
R. S. Maier (2007)
The 192 solutions of the Heun equation,

Math. Comp. 76 (258), pp. 811–843.

External Links:

ISSN 0025-5718, Document, MathReview (Wadim Zudilin), ZentralBlatt (Masaaki Yoshida).

Referenced by:

§31.3(iii).

Encodings:

BibTeX
H. Majima, K. Matsumoto and N. Takayama (2000)
Quadratic relations for confluent hypergeometric functions,

Tohoku Math. J. (2) 52 (4), pp. 489–513.

External Links:

ISSN 0040-8735, Document, MathReview (Takeshi Sasaki), ZentralBlatt.

Referenced by:

§13.12.

Encodings:

BibTeX
K. L. Majumder and G. P. Bhattacharjee (1973)
Algorithm AS 63. The incomplete beta integral,

Appl. Statist. 22 (3), pp. 409–411.

Notes:

Double-precision Fortran. For remark see same journal 26 (1977), pp. 111-114

External Links:

FullText, Code.

Referenced by:

§8.28(iv).

Encodings:

BibTeX
S. Makinouchi (1966)
Zeros of Bessel functions $J_{{\nu}}\,(x)$ and $Y_{{\nu}}\,(x)$ accurate to twenty-nine significant digits,

Technology Reports of the Osaka University 16 (685), pp. 1–44.

Referenced by:

¶ ‣ §10.75(iii).

Encodings:

BibTeX
Yu. I. Manin (1998)
Sixth Painlevé Equation, Universal Elliptic Curve, and Mirror of $\mathbf{P}^{2}$ ,

in Geometry of Differential Equations,

(A. Varchenko and V. Vassiliev Eds.), Amer. Math. Soc. Transl. Ser. 2, Vol. 186, pp. 131–151.

External Links:

MathReview (Bruce Hunt), ZentralBlatt.

Referenced by:

§32.2(iv).

Encodings:

BibTeX
E. L. Mansfield and H. N. Webster (1998)
On one-parameter families of Painlevé III,

Stud. Appl. Math. 101 (3), pp. 321–341.

External Links:

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

Referenced by:

§32.10(iii).

Encodings:

BibTeX
Maple (commercial interactive system)
Maplesoft.

Notes:

General purpose mathematical computing environment. Includes more than 100 special functions. Includes symbolic and arbitrary precision numerical computation.

Referenced by:

§27.22, § ‣ § Software Cross Index.

Encodings:

BibTeX
F. Marcellán, M. Alfaro and M. L. Rezola (1993)
Orthogonal polynomials on Sobolev spaces: Old and new directions,

J. Comput. Appl. Math. 48 (1-2), pp. 113–131.

External Links:

ISSN 0377-0427, Document, MathReview (C. M. Joshi), ZentralBlatt.

Referenced by:

§18.36(ii).

Encodings:

BibTeX
M. Marden (1966)
Geometry of Polynomials,

2nd edition, American Mathematical Society, Providence, RI.

External Links:

ISBN 0821815032, MathReview (O. Shisha), ZentralBlatt.

Referenced by:

§31.15(i), §31.15(ii).

Encodings:

BibTeX
O. I. Marichev (1983)
Handbook of Integral Transforms of Higher Transcendental Functions: Theory and Algorithmic Tables,

Ellis Horwood Ltd./John Wiley & Sons, Inc, Chichester/New York.

Notes:

Edited by F. D. Gakhov, Translated from the Russian by L. W. Longdon

External Links:

ISBN 0-85312-538-7, MathReview, ZentralBlatt.

Referenced by:

§1.14(viii), §10.22(vi), §10.32(iv), §10.43(vi), §10.9(iv), §11.10(x), §11.7(v), §11.9(iv), ¶ ‣ §12.12, §13.10(iii), §13.23(i), §14.17(vi), §15.14, §18.17(ix), §6.14(iii), §7.14(iii), §8.14.

Encodings:

BibTeX
O. I. Marichev (1984)
On the Representation of Meijer’s $G$ -Function in the Vicinity of Singular Unity,

in Complex Analysis and Applications ’81 (Varna, 1981),

pp. 383–398.

External Links:

MathReview (B. D. Agrawal), ZentralBlatt.

Referenced by:

§16.21.

Encodings:

BibTeX
B. Markman (1965)
Contribution no. 14. The Riemann zeta function,

BIT 5, pp. 138–141.

Referenced by:

§25.21(ii).

Encodings:

BibTeX
S. M. Markov (1981)
On the interval computation of elementary functions,

C. R. Acad. Bulgare Sci. 34 (3), pp. 319–322.

External Links:

ISSN 0366-8681, MathReview (David F. Griffiths), ZentralBlatt.

Referenced by:

¶ ‣ §4.45(i).

Encodings:

BibTeX
A. I. Markushevich (1983)
The Theory of Analytic Functions: A Brief Course,

“Mir”, Moscow.

Notes:

Translated from the Russian by Eugene Yankovsky

External Links:

MathReview, ZentralBlatt.

Referenced by:

§1.10(iii), §1.10(vi), §1.9(i), §1.9(iv), §1.9(vi).

Encodings:

BibTeX
A. I. Markushevich (1985)
Theory of Functions of a Complex Variable. Vols. I, II, III,

Chelsea Publishing Co., New York (English).

Notes:

Translated and edited by Richard A. Silverman

External Links:

ISBN 0-8284-0296-5, MathReview, ZentralBlatt.

Referenced by:

§1.9(iv).

Encodings:

BibTeX
A. I. Markushevich (1992)
Introduction to the Classical Theory of Abelian Functions,

American Mathematical Society, Providence, RI.

Notes:

Translated from the 1979 Russian original by G. Bluher

External Links:

ISBN 0-8218-4542-X, MathReview, ZentralBlatt.

Referenced by:

§21.8.

Encodings:

BibTeX
P. Maroni (1995)
An integral representation for the Bessel form,

J. Comput. Appl. Math. 57 (1-2), pp. 251–260.

External Links:

ISSN 0377-0427, Document, MathReview (Hans-Jürgen Glaeske), ZentralBlatt.

Referenced by:

§18.34(ii).

Encodings:

BibTeX
J. E. Marsden and A. J. Tromba (1996)
Vector Calculus,

4th edition, W. H. Freeman & Company, New York.

Notes:

Fifth edition printed in 2003.

External Links:

ISBN 0-7167-2445-6, ZentralBlatt.

Referenced by:

§1.5(i), §1.5(iii), §1.5(v), §1.5(vi), §1.6(i), §1.6(iii), §1.6(iv), §1.6(v).

Encodings:

BibTeX
P. L. Marston (1992)
Geometrical and Catastrophe Optics Methods in Scattering,

in Physical Acoustics,

(R. N. Thurston Ed.), Vol. 21, pp. 1–234.

Referenced by:

§36.14(ii).

Encodings:

BibTeX
P. L. Marston (1999)
Catastrophe optics of spheroidal drops and generalized rainbows,

J. Quantit. Spec. and Rad. Trans. 63, pp. 341–351.

External Links:

Document.

Referenced by:

§36.14(ii).

Encodings:

BibTeX
J. Martinek, H. P. Thielman and E. C. Huebschman (1966)
On the zeros of cross-product Bessel functions,

J. Math. Mech. 16, pp. 447–452.

External Links:

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

Referenced by:

§10.21(x).

Encodings:

BibTeX
B. Martić (1978)
Note sur certaines inégalités d’intégrales,

Akad. Nauka Umjet. Bosne Hercegov. Rad. Odjelj. Prirod. Mat. Nauka 61 (17), pp. 165–168 (French, Serbo-Croatian summary).

External Links:

ISSN 0350-0047, MathReview (V. B. Headley), ZentralBlatt.

Referenced by:

§7.8.

Encodings:

BibTeX
P. Martín, R. Pérez and A. L. Guerrero (1992)
Two-point quasi-fractional approximations to the Airy function $\mathop{\mathrm{Ai}\/}\nolimits(x)$ ,

J. Comput. Phys. 99 (2), pp. 337–340.

Notes:

There is an error in Eq. (5): the second term in parentheses needs to be multiplied by $x$ .

External Links:

ISSN 0021-9991, Document, MathReview Entry, ZentralBlatt.

Referenced by:

§9.19(i).

Encodings:

BibTeX
J. C. Mason and D. C. Handscomb (2003)
Chebyshev Polynomials,

Chapman & Hall/CRC, Boca Raton, FL.

External Links:

ISBN 0-8493-0355-9, MathReview, ZentralBlatt.

Referenced by:

¶ ‣ §18.3, ¶ ‣ §18.38(i), ¶ ‣ §18.38(i), §18.40, ¶ ‣ §3.11(ii), ¶ ‣ §3.11(ii), §3.11(ii), §3.3(vi), §3.5(iv).

Encodings:

BibTeX
D. R. Masson (1991)
Associated Wilson polynomials,

Constr. Approx. 7 (4), pp. 521–534.

External Links:

ISSN 0176-4276, Document, MathReview (R. A. Askey), ZentralBlatt.

Referenced by:

§16.4(iii).

Encodings:

BibTeX
T. Masuda, Y. Ohta and K. Kajiwara (2002)
A determinant formula for a class of rational solutions of Painlevé V equation,

Nagoya Math. J. 168, pp. 1–25.

External Links:

ISSN 0027-7630, MathReview (Andrei A. Kapaev), ZentralBlatt.

Referenced by:

§32.8(v).

Encodings:

BibTeX
T. Masuda (2003)
On a class of algebraic solutions to the Painlevé VI equation, its determinant formula and coalescence cascade,

Funkcial. Ekvac. 46 (1), pp. 121–171.

External Links:

ISSN 0532-8721, FullText, MathReview (Andrew Pickering), ZentralBlatt.

Referenced by:

§32.9(iii).

Encodings:

BibTeX
T. Masuda (2004)
Classical transcendental solutions of the Painlevé equations and their degeneration,

Tohoku Math. J. (2) 56 (4), pp. 467–490.

External Links:

ISSN 0040-8735, Document, MathReview (Oleg Gleizer), ZentralBlatt.

Referenced by:

§32.10(v), §32.10(vi).

Encodings:

BibTeX
A. M. Mathai (1993)
A Handbook of Generalized Special Functions for Statistical and Physical Sciences,

Oxford Science Publications, The Clarendon Press Oxford University Press, New York.

External Links:

ISBN 0-19-853595-3, MathReview (W. A. Al-Salam), ZentralBlatt.

Referenced by:

§16.18, §16.19, §16.20.

Encodings:

BibTeX
Mathematica (commercial interactive system)
Wolfram Research, Inc..

Notes:

General purpose mathematical computing environment with broad coverage of special functions, including complex arguments and parameters. Includes symbolic and arbitrary precision numerical computation.

Referenced by:

§27.22, § ‣ § Software Cross Index.

Encodings:

BibTeX
Matlab (commercial interactive system)
The MathWorks, Inc..

Notes:

General purpose mathematical computing environment. Includes a collection of special functions. Computations in double precision with symbolic and extended-precision capabilities available.

Referenced by:

§ ‣ § Software Cross Index.

Encodings:

BibTeX
F. Matta and A. Reichel (1971)
Uniform computation of the error function and other related functions,

Math. Comp. 25 (114), pp. 339–344.

External Links:

FullText, MathReview, ZentralBlatt.

Referenced by:

§7.22(i).

Encodings:

BibTeX
D. W. Matula and P. Kornerup (1980)
Foundations of Finite Precision Rational Arithmetic,

(R. D. Grigorieff Ed.), Comput. Suppl., Vol. 2, Vienna, pp. 85–111.

External Links:

MathReview (G. Blanch), ZentralBlatt.

Referenced by:

§3.1(iii).

Encodings:

BibTeX
G. Matviyenko (1993)
On the evaluation of Bessel functions,

Appl. Comput. Harmon. Anal. 1 (1), pp. 116–135.

External Links:

ISSN 1063-5203, Document, MathReview, ZentralBlatt.

Referenced by:

§10.77(iii).

Encodings:

BibTeX
Maxima (free interactive system)

Notes:

System for the manipulation of symbolic and numerical expressions. Includes a collection of special functions. Utilizes exact fractions, arbitrary precision integers, and arbitrary precision floating point numbers.

External Links:

Home Page.

Referenced by:

§ ‣ § Software Cross Index.

Encodings:

BibTeX
L. C. Maximon (1955)
On the evaluation of indefinite integrals involving the special functions: Application of method,

Quart. Appl. Math. 13, pp. 84–93.

External Links:

MathReview (A. Erdélyi), ZentralBlatt.

Referenced by:

§14.17(i).

Encodings:

BibTeX
L. C. Maximon (1991)
On the evaluation of the integral over the product of two spherical Bessel functions,

J. Math. Phys. 32 (3), pp. 642–648.

External Links:

ISSN 0022-2488, Document, MathReview (S. K. Chatterjea), ZentralBlatt.

Referenced by:

¶ ‣ §1.17(ii), §10.59.

Encodings:

BibTeX
L. C. Maximon (2003)
The dilogarithm function for complex argument,

Proc. Roy. Soc. London Ser. A 459, pp. 2807–2819.

External Links:

ISSN 1364-5021, Document, MathReview (Wadim Zudilin), ZentralBlatt.

Referenced by:

¶ ‣ §25.12(ii), §25.12(i), §25.12(i), §25.12(i).

Encodings:

BibTeX
M. Mazzocco (2001a)
Rational solutions of the Painlevé VI equation,

J. Phys. A 34 (11), pp. 2281–2294.

External Links:

ISSN 0305-4470, Document, MathReview (Shun Shimomura), ZentralBlatt.

Referenced by:

§32.8(vi).

Encodings:

BibTeX
M. Mazzocco (2001b)
Picard and Chazy solutions to the Painlevé VI equation,

Math. Ann. 321 (1), pp. 157–195.

External Links:

ISSN 0025-5831, Document, MathReview, ZentralBlatt.

Referenced by:

§32.9(iii).

Encodings:

BibTeX
R. C. McCann (1977)
Inequalities for the zeros of Bessel functions,

SIAM J. Math. Anal. 8 (1), pp. 166–170.

External Links:

ISSN 1095-7154, Document, MathReview (Mary L. Boas), ZentralBlatt.

Referenced by:

§10.21(iv).

Encodings:

BibTeX
J. P. McClure and R. Wong (1978)
Explicit error terms for asymptotic expansions of Stieltjes transforms,

J. Inst. Math. Appl. 22 (2), pp. 129–145.

External Links:

ISSN 0020-2932, Document, MathReview (G. M. Habibullah), ZentralBlatt.

Referenced by:

§2.6(ii).

Encodings:

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J. P. McClure and R. Wong (1979)
Exact remainders for asymptotic expansions of fractional integrals,

J. Inst. Math. Appl. 24 (2), pp. 139–147.

External Links:

ISSN 0020-2932, Document, MathReview, ZentralBlatt.

Referenced by:

¶ ‣ §2.6(iii).

Encodings:

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J. P. McClure and R. Wong (1987)
Asymptotic expansion of a multiple integral,

SIAM J. Math. Anal. 18 (6), pp. 1630–1637.

External Links:

ISSN 0036-1410, Document, MathReview (E. Riekstiņš), ZentralBlatt.

Referenced by:

§2.5(ii).

Encodings:

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B. M. McCoy, C. A. Tracy and T. T. Wu (1977)
Painlevé functions of the third kind,

J. Mathematical Phys. 18 (5), pp. 1058–1092.

External Links:

Document, MathReview, ZentralBlatt.

Referenced by:

§32.11(iv), ¶ ‣ §32.16, §32.2(iii).

Encodings:

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B. M. McCoy (1992)
Spin Systems, Statistical Mechanics and Painlevé Functions,

in Painlevé Transcendents: Their Asymptotics and Physical Applications,

(P. Winternitz Ed.), NATO Adv. Sci. Inst. Ser. B Phys., Vol. 278, pp. 377–391.

Notes:

Proc. NATO Adv. Res. Workshop, Sainte-Adèle, Canada, 1990

External Links:

MathReview, ZentralBlatt.

Referenced by:

¶ ‣ §32.16.

Encodings:

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F. A. McDonald and J. Nuttall (1969)
Complex-energy method for elastic $e$ -H scattering above the ionization threshold,

Phys. Rev. Lett. 23 (7), pp. 361–363.

External Links:

Document.

Referenced by:

§33.22(vii).

Encodings:

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J. N. McDonald and N. A. Weiss (1999)
A Course in Real Analysis,

Academic Press Inc., San Diego, CA.

External Links:

ISBN 0-12-742830-5, MathReview (Sherif T. El-Helaly), ZentralBlatt.

Referenced by:

¶ ‣ §18.2(i).

Encodings:

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H. R. McFarland and D. St. P. Richards (2001)
Exact misclassification probabilities for plug-in normal quadratic discriminant functions. I. The equal-means case,

J. Multivariate Anal. 77 (1), pp. 21–53.

External Links:

ISSN 0047-259X, Document, MathReview (Peter A. Lachenbruch), ZentralBlatt.

Referenced by:

§35.9.

Encodings:

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H. R. McFarland and D. St. P. Richards (2002)
Exact misclassification probabilities for plug-in normal quadratic discriminant functions. II. The heterogeneous case,

J. Multivariate Anal. 82 (2), pp. 299–330.

External Links:

ISSN 0047-259X, Document, MathReview (Peter A. Lachenbruch), ZentralBlatt.

Referenced by:

§35.9.

Encodings:

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H. McKean and V. Moll (1999)
Elliptic Curves,

Cambridge University Press, Cambridge.

Notes:

Reprint with corrections of original edition, published in 1997 by Cambridge University Press

External Links:

ISBN 0-521-58228-8; 0-521-65817-9, MathReview (Amílcar Pacheco), ZentralBlatt.

Referenced by:

¶ ‣ §20.1, §20.11(i), §20.11(ii), §20.12(i), §20.12(i), §20.12(ii), §20.7(iii), §20.7(v), §20.9(i), §20.9(ii), Ch.20, §22.18(ii), §22.18(iv), Ch.22, ¶ ‣ §23.1, §23.15(i), §23.20(i), §23.20(ii), §23.20(ii), §23.21(ii), ¶ ‣ §23.22(ii), ¶ ‣ §23.6(iv), Ch.23.

Encodings:

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N. M. McLachlan and A. L. Meyers (1936)
The ster and stei functions,

Phil. Mag. Series 7 21 (140), pp. 425–436.

External Links:

Document, ZentralBlatt.

Referenced by:

§11.8.

Encodings:

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N. W. McLachlan (1934)
Loud Speakers: Theory, Performance, Testing and Design,

Oxford University Press, New York.

Notes:

Reprinted, with corrections, by Dover Publications Inc., 1960.

External Links:

MathReview, ZentralBlatt.

Referenced by:

§11.12.

Encodings:

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N. W. McLachlan (1947)
Theory and Application of Mathieu Functions,

Clarendon Press, Oxford.

Notes:

Corrected republication by Dover Publications, Inc., New York, 1964.

External Links:

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

Referenced by:

¶ ‣ §28.1, §28.2(i), §28.29(i), §28.33(ii), §28.33(iii), §28.33(ii), §28.4(vi), §28.4(vi), ¶ ‣ §28.5(i), §28.5(i), §28.9, Ch.28.

Encodings:

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N. W. McLachlan (1961)
Bessel Functions for Engineers,

2nd edition, Clarendon Press, Oxford.

Notes:

The first edition was published in 1934 by Clarendon Press. The second edition was published originally in 1955.

External Links:

ZentralBlatt.

Referenced by:

§10.73(iii).

Encodings:

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J. McMahon (1894)
On the roots of the Bessel and certain related functions,

Ann. of Math. 9 (1-6), pp. 23–30.

External Links:

ISSN 0003-486X, FullText, MathReview Entry, ZentralBlatt.

Referenced by:

§10.21(x).

Encodings:

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J. M. McNamee (2007)
Numerical Methods for Roots of Polynomials. Part I,

Studies in Computational Mathematics, Vol. 14, Elsevier, Amsterdam.

External Links:

ISBN 978-0-444-52729-5; 0-444-52729-X, MathReview Entry, ZentralBlatt.

Referenced by:

¶ ‣ §3.8(iv).

Encodings:

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Fr. Mechel (1966)
Calculation of the modified Bessel functions of the second kind with complex argument,

Math. Comp. 20 (95), pp. 407–412.

External Links:

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

Referenced by:

§10.74(iii).

Encodings:

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V. Meden and K. Schönhammer (1992)
Spectral functions for the Tomonaga-Luttinger model,

Phys. Rev. B 46 (24), pp. 15753–15760.

External Links:

Document.

Referenced by:

§13.28(iii).

Encodings:

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D. S. Meek and D. J. Walton (1992)
Clothoid spline transition spirals,

Math. Comp. 59 (199), pp. 117–133.

External Links:

ISSN 0025-5718, Document, MathReview, ZentralBlatt.

Referenced by:

§7.21.

Encodings:

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R. Mehrem, J. T. Londergan and M. H. Macfarlane (1991)
Analytic expressions for integrals of products of spherical Bessel functions,

J. Phys. A 24 (7), pp. 1435–1453.

External Links:

ISSN 0305-4470, Document, MathReview, ZentralBlatt.

Referenced by:

§10.59.

Encodings:

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M. L. Mehta (2004)
Random Matrices,

3rd edition, Pure and Applied Mathematics (Amsterdam), Vol. 142, Elsevier/Academic Press, Amsterdam.

External Links:

ISBN 0-12-088409-7, MathReview, ZentralBlatt.

Referenced by:

§5.14, ¶ ‣ §5.20, §5.20.

Encodings:

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C. S. Meijer (1946)
On the $G$ -function. VII, VIII,

Nederl. Akad. Wetensch., Proc. 49, pp. 1063–1072, 1165–1175 = Indagationes Math. 8, 661–670, 713–723 (1946).

External Links:

MathReview (A. Erdélyi), ZentralBlatt.

Referenced by:

§16.11(ii).

Encodings:

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J. W. Meijer and N. H. G. Baken (1987)
The exponential integral distribution,

Statist. Probab. Lett. 5 (3), pp. 209–211.

External Links:

ISSN 0167-7152, Document, MathReview Entry, ZentralBlatt.

Referenced by:

§8.19(xi).

Encodings:

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G. Meinardus (1967)
Approximation of Functions: Theory and Numerical Methods,

Springer Tracts in Natural Philosophy, Vol. 13, Springer-Verlag, New York.

Notes:

Expanded translation from the German edition. Translated by Larry L. Schumaker

External Links:

MathReview, ZentralBlatt.

Referenced by:

§3.11(i), §3.11(iii).

Encodings:

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P. N. Meisinger, T. R. Miller and M. C. Ogilvie (2002)
Phenomenological equations of state for the quark-gluon plasma,

Phys. Rev. D 65 (3), pp. (034009–1)–(034009–10).

External Links:

Document.

Referenced by:

§24.18.

Encodings:

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J. Meixner, F. W. Schäfke and G. Wolf (1980)
Mathieu Functions and Spheroidal Functions and Their Mathematical Foundations: Further Studies,

Lecture Notes in Mathematics, Vol. 837, Springer-Verlag, Berlin-New York.

External Links:

ISBN 3-540-10282-5, 0-387-10282-5, MathReview (R. A. Askey), ZentralBlatt.

Referenced by:

§28.10(ii), §28.11, §28.2(v), §28.27, §28.28(i), §28.28(v), §28.30(ii), §28.6(i), §28.6(i), §28.6(i), §28.7, §28.7, Ch.28, §30.11(vi), §30.12, §30.13(v), §30.14(v), §30.15(i), §30.3(iv), Ch.30, Gerhard Wolf.

Encodings:

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J. Meixner and F. W. Schäfke (1954)
Mathieusche Funktionen und Sphäroidfunktionen mit Anwendungen auf physikalische und technische Probleme,

Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete, Band LXXI, Springer-Verlag, Berlin (German).

External Links:

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

Referenced by:

Table 28.1.1, §28.10(i), §28.11, §28.12(i), §28.12(ii), §28.12(iii), §28.14, §28.15(i), §28.15(ii), §28.16, §28.17, §28.19, §28.2(ii), §28.2(iii), §28.2(iv), §28.2(v), §28.2(vi), §28.20(ii), §28.20(iii), §28.20(vi), §28.20(vii), §28.22(i), §28.22(ii), §28.23, §28.24, §28.25, §28.28(i), §28.33(ii), §28.33(iii), §28.33(ii), §28.34(ii), §28.34(iii), §28.4(i), §28.4(ii), §28.4(iii), §28.4(iv), §28.4(v), §28.4(vi), §28.4(vi), ¶ ‣ §28.5(i), §28.5(i), §28.6(i), §28.6(ii), §28.7, §28.7, §28.8(i), §28.8(ii), §28.9, Ch.28, §30.1, §30.10, §30.11(iii), §30.11(iii), §30.11(iv), §30.11(v), §30.11(vi), §30.11(vi), §30.13(i), §30.13(ii), §30.13(iii), §30.13(iv), §30.13(v), §30.13(v), §30.14(i), §30.14(ii), §30.14(iii), §30.14(iv), §30.14(v), §30.14(v), §30.16(i), §30.16(i), §30.2(i), §30.2(ii), §30.3(i), §30.3(ii), §30.3(iii), §30.3(iv), §30.4(i), §30.4(ii), §30.4(iv), §30.5, §30.5, ¶ ‣ §30.6, §30.6, §30.8(i), §30.8(ii), §30.9(i), §30.9(i), §30.9(ii), §30.9(ii), Ch.30.

Encodings:

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J. Meixner (1951)
Klassifikation, Bezeichnung und Eigenschaften der Sphäroidfunktionen,

Math. Nachr. 5, pp. 1–18 (German).

External Links:

Document, MathReview (F. Oberhettinger), ZentralBlatt.

Referenced by:

§30.10.

Encodings:

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J. Meixner (1944)
Die Laméschen Wellenfunktionen des Drehellipsoids,

Forschungsbericht No. 1952

ZWB (German).

Notes:

English translation: Lamé wave functions of the ellipsoid of revolution appeared as NACA Technical Memorandum No. 1224, 1949

External Links:

MathReview.

Referenced by:

§30.9(iii).

Encodings:

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A. J. Menezes, P. C. van Oorschot and S. A. Vanstone (1997)
Handbook of Applied Cryptography,

CRC Press, Boca Raton, FL.

Notes:

With a foreword by Ronald L. Rivest

External Links:

ISBN 0-8493-8523-7, MathReview (Yvo Desmedt), ZentralBlatt.

Referenced by:

§27.16.

Encodings:

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A. McD. Mercer (1992)
The zeros of $az^{2}{\mathop{J_{{\nu}}\/}\nolimits^{{\prime\prime}}}\!\left(z\right)+bz{\mathop{J_{{\nu}}\/}\nolimits^{{\prime}}}\!\left(z\right)+c\mathop{J_{{\nu}}\/}\nolimits\!\left(z\right)$ as functions of order,

Internat. J. Math. Math. Sci. 15 (2), pp. 319–322.

External Links:

ISSN 0161-1712, Document, MathReview (Andrea Laforgia), ZentralBlatt.

Referenced by:

§10.21(iv).

Encodings:

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J. N. Merner (1962)
Algorithm 149: Complete elliptic integral,

Comm. ACM 5 (12), pp. 605.

Notes:

Includes Algol program, maximum accuracy 10D. For remark see ACM Trans. Math. Software 4 (1978), p. 95

External Links:

ISSN 0001-0782, Document.

Referenced by:

§19.39(ii).

Encodings:

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X. Merrheim (1994)
The computation of elementary functions in radix $2^{p}$ ,

Computing 53 (3-4), pp. 219–232.

Notes:

International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (Vienna, 1993)

External Links:

ISSN 0010-485X, Document, MathReview, ZentralBlatt.

Referenced by:

¶ ‣ §4.45(i).

Encodings:

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A. Messiah (1961)
Quantum Mechanics. Vol. I,

North-Holland Publishing Co., Amsterdam.

Notes:

Translated from the French by G. M. Temmer

External Links:

MathReview (A. S. Wightman), ZentralBlatt.

Referenced by:

§10.73(ii).

Encodings:

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R. Metzler, J. Klafter and J. Jortner (1999)
Hierarchies and logarithmic oscillations in the temporal relaxation patterns of proteins and other complex systems,

Proc. Nat. Acad. Sci. U .S. A. 96 (20), pp. 11085–11089.

External Links:

FullText.

Referenced by:

§8.24(i).

Encodings:

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A. Michaeli (1996)
Asymptotic analysis of edge-excited currents on a convex face of a perfectly conducting wedge under overlapping penumbra region conditions,

IEEE Trans. Antennas and Propagation 44 (1), pp. 97–101.

External Links:

Document.

Referenced by:

§9.14.

Encodings:

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N. Michel and M. V. Stoitsov (2008)
Fast computation of the Gauss hypergeometric function with all its parameters complex with application to the Pöschl-Teller-Ginocchio potential wave functions,

Comput. Phys. Comm. 178 (7), pp. 535–551.

External Links:

ISSN 0010-4655, Document, FullText, MathReview Entry, ZentralBlatt.

Referenced by:

§15.19(i), §15.19(i).

Encodings:

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N. Michel (2007)
Precise Coulomb wave functions for a wide range of complex $\ell$ , $\eta$ and $z$ ,

Computer Physics Communications 176 (3), pp. 232–249.

Notes:

C++ code. Maximum accuracy 10D

External Links:

Document, Code.

Referenced by:

§33.26(iii).

Encodings:

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C. Micu and E. Papp (2005)
Applying $q$ -Laguerre polynomials to the derivation of $q$ -deformed energies of oscillator and Coulomb systems,

Romanian Reports in Physics 57 (1), pp. 25–34.

Referenced by:

§17.17.

Encodings:

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M. Micu (1968)
Recursion relations for the 3- $j$ symbols,

Nuclear Physics A 113 (1), pp. 215–220.

External Links:

Document.

Referenced by:

§34.3(iii).

Encodings:

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P. Midy (1975)
An improved calculation of the general elliptic integral of the second kind in the neighbourhood of $x=0$ ,

Numer. Math. 25 (1), pp. 99–101.

External Links:

ISSN 0029-599X, Document, MathReview (Roland Bulirsch), ZentralBlatt.

Referenced by:

¶ ‣ §19.36(ii).

Encodings:

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G. J. Miel (1981)
Evaluation of complex logarithms and related functions,

SIAM J. Numer. Anal. 18 (4), pp. 744–750.

External Links:

ISSN 0036-1429, Document, MathReview (M. Brannigan), ZentralBlatt.

Referenced by:

§4.45(ii).

Encodings:

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J. W. Miles (1978)
On the second Painlevé transcendent,

Proc. Roy. Soc. London Ser. A 361, pp. 277–291.

External Links:

ISSN 0080-4630, FullText, MathReview (Mark J. Ablowitz), ZentralBlatt.

Referenced by:

§32.11(ii), §32.17, §32.3(ii).

Encodings:

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J. W. Miles (1975)
Asymptotic approximations for prolate spheroidal wave functions,

Studies in Appl. Math. 54 (4), pp. 315–349.

External Links:

MathReview (M. L. Mehta), ZentralBlatt.

Referenced by:

§30.9(i).

Encodings:

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J. W. Miles (1980)
The Second Painlevé Transcendent: A Nonlinear Airy Function,

in Mechanics Today,

Vol. 5, pp. 297–313.

External Links:

MathReview (H. E. Fettis), ZentralBlatt.

Referenced by:

§32.11(ii), §32.17, §32.3(ii).

Encodings:

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M. S. Milgram (1985)
The generalized integro-exponential function,

Math. Comp. 44 (170), pp. 443–458.

External Links:

ISSN 0025-5718, FullText, MathReview (S. Conde), ZentralBlatt.

Referenced by:

¶ ‣ §8.19(v), §8.19(xi).

Encodings:

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A. R. Miller (1997)
A class of generalized hypergeometric summations,

J. Comput. Appl. Math. 87 (1), pp. 79–85.

External Links:

ISSN 0377-0427, Document, MathReview, ZentralBlatt.

Referenced by:

§16.10.

Encodings:

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A. R. Miller (2003)
On a Kummer-type transformation for the generalized hypergeometric function ${}_{2}F_{2}$ ,

J. Comput. Appl. Math. 157 (2), pp. 507–509.

External Links:

ISSN 0377-0427, Document, MathReview Entry, ZentralBlatt.

Referenced by:

¶ ‣ §16.6.

Encodings:

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G. F. Miller (1960)
Tables of Generalized Exponential Integrals,

NPL Mathematical Tables, Vol. III, Her Majesty’s Stationery Office, London.

External Links:

MathReview (L. Fox).

Referenced by:

§8.25(v).

Encodings:

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G. F. Miller (1966)
On the convergence of the Chebyshev series for functions possessing a singularity in the range of representation,

SIAM J. Numer. Anal. 3 (3), pp. 390–409.

External Links:

ISSN 1095-7170, Document, MathReview (Y. L. Luke), ZentralBlatt.

Referenced by:

¶ ‣ §3.11(ii).

Encodings:

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J. C. P. Miller (1946)
The Airy Integral, Giving Tables of Solutions of the Differential Equation $y^{{\prime\prime}}=xy$ ,

British Association for the Advancement of Science, Mathematical Tables Part-Vol. B, Cambridge University Press, Cambridge.

External Links:

MathReview (C. J. Bouwkamp), ZentralBlatt.

Referenced by:

§9.18(ii), §9.18(iv), §9.2(i), §9.2(ii), §9.2(v), §9.4, §9.5(i), §9.6(i), §9.8(i), §9.8(ii), §9.8(iv), §9.9(ii), Ch.9.

Encodings:

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J. C. P. Miller (1950)
On the choice of standard solutions for a homogeneous linear differential equation of the second order,

Quart. J. Mech. Appl. Math. 3 (2), pp. 225–235.

External Links:

Document, MathReview (W. R. Wasow), ZentralBlatt.

Referenced by:

§12.2(vi), §2.7(iv), §2.7(iv).

Encodings:

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J. C. P. Miller (1952)
On the choice of standard solutions to Weber’s equation,

Proc. Cambridge Philos. Soc. 48, pp. 428–435.

External Links:

Document, MathReview (W. Wasow), ZentralBlatt.

Referenced by:

§12.1, §12.14(i), §12.2(i).

Encodings:

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J. C. P. Miller (Ed.) (1955)
Tables of Weber Parabolic Cylinder Functions,

Her Majesty’s Stationery Office, London.

External Links:

MathReview (A. Erdélyi), ZentralBlatt.

Referenced by:

§10.16, ¶ ‣ §10.39, §12.14(i), §12.14(x), §12.14(x), §12.14(ii), §12.14(iv), §12.14(v), §12.14(v), §12.14(vi), §12.14(vii), §12.14(viii), §12.19, §12.2(i), §12.2(ii), §12.2(iii), §12.2(iv), §12.2(v), §12.2(vi), §12.2(vi), §12.4, §12.5(i), §12.5(ii), §12.5(iii), §12.7(i), §12.7(ii), §12.7(iii), §12.7(iii), §12.7(iv), §12.8(i), Ch.12.

Encodings:

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J. Miller and V. S. Adamchik (1998)
Derivatives of the Hurwitz zeta function for rational arguments,

J. Comput. Appl. Math. 100 (2), pp. 201–206.

External Links:

ISSN 0377-0427, Document, MathReview, ZentralBlatt.

Referenced by:

§25.11(vi), §25.18(i), §25.6(ii).

Encodings:

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W. Miller (1974)
Lie theory and separation of variables. I: Parabolic cylinder coordinates,

SIAM J. Math. Anal. 5 (4), pp. 626–643.

External Links:

Document, MathReview (G. R. Allcock), ZentralBlatt.

Referenced by:

§12.13(ii), §12.17.

Encodings:

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W. Miller (1977)
Symmetry and Separation of Variables,

Addison-Wesley Publishing Co., Reading, MA-London-Amsterdam.

Notes:

Encyclopedia of Mathematics and its Applications, Vol. 4

External Links:

ISBN 0-201-13503-5, MathReview (Ernest G. Kalnins), ZentralBlatt.

Referenced by:

§31.17(i).

Encodings:

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J. P. Mills (1926)
Table of the ratio: Area to bounding ordinate, for any portion of normal curve,

Biometrika 18, pp. 395–400.

External Links:

FullText, ZentralBlatt.

Referenced by:

§7.8.

Encodings:

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A. E. Milne, P. A. Clarkson and A. P. Bassom (1997)
Bäcklund transformations and solution hierarchies for the third Painlevé equation,

Stud. Appl. Math. 98 (2), pp. 139–194.

External Links:

ISSN 0022-2526, Document, MathReview (Alexander Vladimirovich Kitaev), ZentralBlatt.

Referenced by:

§32.10(iii), §32.7(iii), §32.8(iii), §32.9(i).

Encodings:

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S. C. Milne (1985a)
A $q$ -analog of the $\mathop{{{}_{{5}}F_{{4}}}\/}\nolimits\!\left(;;1\right)$ summation theorem for hypergeometric series well-poised in $SU(n)$ ,

Adv. in Math. 57 (1), pp. 14–33.

External Links:

ISSN 0001-8708, Document, MathReview (Mourad E. H. Ismail), ZentralBlatt.

Referenced by:

§17.15.

Encodings:

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S. C. Milne (1985b)
An elementary proof of the Macdonald identities for $A_{l}^{{(1)}}$ ,

Adv. in Math. 57 (1), pp. 34–70.

External Links:

ISSN 0001-8708, Document, MathReview (Y. Lehrer-Ilamed), ZentralBlatt.

Referenced by:

§17.15.

Encodings:

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S. C. Milne (1985c)
A new symmetry related to $SU(n)$ for classical basic hypergeometric series,

Adv. in Math. 57 (1), pp. 71–90.

External Links:

ISSN 0001-8708, Document, MathReview (George E. Andrews), ZentralBlatt.

Referenced by:

§17.15.

Encodings:

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S. C. Milne (1985d)
A $q$ -analog of hypergeometric series well-poised in $SU(n)$ and invariant $G$ -functions,

Adv. in Math. 58 (1), pp. 1–60.

External Links:

ISSN 0001-8708, Document, MathReview (Robert A. Gustafson), ZentralBlatt.

Referenced by:

§17.15.

Encodings:

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S. C. Milne (1988)
A $q$ -analog of the Gauss summation theorem for hypergeometric series in $U(n)$ ,

Adv. in Math. 72 (1), pp. 59–131.

External Links:

ISSN 0001-8708, Document, MathReview (David M. Bressoud), ZentralBlatt.

Referenced by:

§17.15.

Encodings:

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S. C. Milne (1994)
A $q$ -analog of a Whipple’s transformation for hypergeometric series in $U(n)$ ,

Adv. Math. 108 (1), pp. 1–76.

External Links:

ISSN 0001-8708, Document, MathReview, ZentralBlatt.

Referenced by:

§17.15.

Encodings:

BibTeX
S. C. Milne (2002)
Infinite families of exact sums of squares formulas, Jacobi elliptic functions, continued fractions, and Schur functions,

Ramanujan J. 6 (1), pp. 7–149.

External Links:

Document, ZentralBlatt.

Referenced by:

§27.13(iv).

Encodings:

BibTeX
S. C. Milne and G. M. Lilly (1992)
The $A_{{l}}$ and $C_{{l}}$ Bailey transform and lemma,

Bull. Amer. Math. Soc. (N.S.) 26 (2), pp. 258–263.

External Links:

ISSN 0273-0979, Pdf, Document, MathReview (Robert A. Gustafson), ZentralBlatt.

Referenced by:

¶ ‣ §17.12.

Encodings:

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S. C. Milne (1996)
New infinite families of exact sums of squares formulas, Jacobi elliptic functions, and Ramanujan’s tau function,

Proc. Nat. Acad. Sci. U.S.A. 93 (26), pp. 15004–15008.

External Links:

ISSN 0027-8424, MathReview (Ken Ono), ZentralBlatt.

Referenced by:

§27.13(iv).

Encodings:

BibTeX
S. C. Milne (1997)
Balanced $\sideset{{}_{3}}{{}_{2}}{\mathop{\Theta}}$ summation theorems for $U(n)$ basic hypergeometric series,

Adv. Math. 131 (1), pp. 93–187.

External Links:

ISSN 0001-8708, Document, MathReview (Jiang Zeng), ZentralBlatt.

Referenced by:

§17.15.

Encodings:

BibTeX
L. M. Milne-Thomson (1933)
The Calculus of Finite Differences,

Macmillan and Co. Ltd., London.

Notes:

Reprinted in 1951 by Macmillan, and in 1981 by Chelsea Publishing Co., New York, and American Mathematical Society, AMS Chelsea Book Series, Providence, RI.

External Links:

ZentralBlatt.

Referenced by:

¶ ‣ §24.16(i), ¶ ‣ §24.17(i), §24.2(i), §24.2(ii), §24.4(i), §24.4(ii), §24.4(iii), §24.4(v), ¶ ‣ §26.1, ¶ ‣ §26.1.

Encodings:

BibTeX
L. M. Milne-Thomson (1950)
Jacobian Elliptic Function Tables,

Dover Publications Inc., New York.

External Links:

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

Referenced by:

§22.20(vii).

Encodings:

BibTeX
A. C. G. Mitchell and M. W. Zemansky (1961)
Resonance Radiation and Excited Atoms,

2nd edition, Cambridge Univerity Press, Cambridge, England.

Notes:

Reprinted by Cambridge University Press in 1971.

External Links:

FullText, ZentralBlatt.

Referenced by:

§7.21.

Encodings:

BibTeX
D. S. Mitrinović (1964)
Elementary Inequalities,

P. Noordhoff Ltd., Groningen.

Notes:

In cooperation with E. S. Barnes, D. C. B. Marsh, J. R. M. Radok. Tutorial Text, No. 1

External Links:

MathReview (N. D. Kazarinoff), ZentralBlatt.

Referenced by:

¶ ‣ §4.18, §4.32, §4.5(i), §4.5(ii).

Encodings:

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D. S. Mitrinović (1970)
Analytic Inequalities,

Springer-Verlag, New York.

Notes:

Addenda: Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz., no. 634–677 (1979), pp. 3–24 and no. 577-598 (1977), pp. 3–10.

External Links:

MathReview (R. A. Askey and R. P. Boas, Jr.), ZentralBlatt.

Referenced by:

¶ ‣ §4.18, §4.32, §4.5(i), §4.5(ii), §7.8.

Encodings:

BibTeX
D. S. Moak (1981)
The $q$ -analogue of the Laguerre polynomials,

J. Math. Anal. Appl. 81 (1), pp. 20–47.

External Links:

ISSN 0022-247X, Document, MathReview (R. A. Askey).

Referenced by:

§18.27(v).

Encodings:

BibTeX
D. S. Moak (1984)
The $q$ -analogue of Stirling’s formula,

Rocky Mountain J. Math. 14 (2), pp. 403–413.

External Links:

ISSN 0035-7596, MathReview (David M. Bressoud), ZentralBlatt.

Referenced by:

§5.18(ii).

Encodings:

BibTeX
S. Moch, P. Uwer and S. Weinzierl (2002)
Nested sums, expansion of transcendental functions, and multiscale multiloop integrals,

J. Math. Phys. 43 (6), pp. 3363–3386.

External Links:

ISSN 0022-2488, Document, MathReview (Driss Essouabri), ZentralBlatt.

Referenced by:

§16.24(ii).

Encodings:

BibTeX
V. P. Modenov and A. V. Filonov (1986)
Calculation of zeros of cylindrical functions and their derivatives,

Vestnik Moskov. Univ. Ser. XV Vychisl. Mat. Kibernet. (2), pp. 63–64, 71 (Russian).

Notes:

In Russian

External Links:

ISSN 0137-0782, MathReview, ZentralBlatt.

Referenced by:

¶ ‣ §10.74(vi).

Encodings:

BibTeX
N. Mohankumar and A. Natarajan (1997)
The accurate evaluation of a particular Fermi-Dirac integral,

Comput. Phys. Comm. 101 (1-2), pp. 47–53.

External Links:

Document, ZentralBlatt.

Referenced by:

§25.18(i).

Encodings:

BibTeX
E. W. Montroll (1964)
Lattice Statistics,

in Applied Combinatorial Mathematics,

University of California Engineering and Physical Sciences Extension Series, pp. 96–143.

Notes:

Reprinted by Robert E. Krieger Publishing Co. in 1981.

External Links:

ZentralBlatt.

Referenced by:

§26.20.

Encodings:

BibTeX
P. Moon and D. E. Spencer (1971)
Field Theory Handbook. Including Coordinate Systems, Differential Equations and Their Solutions,

2nd edition, Springer-Verlag, Berlin.

Notes:

Reprinted in 1988.

External Links:

ISBN 3-540-18430-9, MathReview.

Referenced by:

Table 28.1.1.

Encodings:

BibTeX
R. J. Moore (1982)
Algorithm AS 187. Derivatives of the incomplete gamma integral,

Appl. Statist. 31 (3), pp. 330–335.

Notes:

Single-precision Fortran.

External Links:

FullText, Code, Document, ZentralBlatt.

Referenced by:

§8.28(ii).

Encodings:

BibTeX
R. E. Moore (1979)
Methods and Applications of Interval Analysis,

SIAM Studies in Applied Mathematics, Vol. 2, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.

External Links:

ISBN 0-89871-161-4, MathReview (H. Ratschek), ZentralBlatt.

Referenced by:

§3.1(ii).

Encodings:

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L. J. Mordell (1917)
On the representation of numbers as a sum of $2r$ squares,

Quarterly Journal of Math. 48, pp. 93–104.

Referenced by:

§27.13(iv).

Encodings:

BibTeX
L. J. Mordell (1958)
On the evaluation of some multiple series,

J. London Math. Soc. (2) 33, pp. 368–371.

External Links:

Document, MathReview (V. F. Cowling), ZentralBlatt.

Referenced by:

§25.6(i).

Encodings:

BibTeX
G. W. Morgenthaler and H. Reismann (1963)
Zeros of first derivatives of Bessel functions of the first kind, $J_{{n}}^{{\prime}}\,(x)$ , $21\leq n\leq 51$ , $0\leq x\leq 100$ ,

J. Res. Nat. Bur. Standards Sect. B 67B (3), pp. 181–183.

External Links:

ISSN 0160-1741, MathReview, ZentralBlatt.

Referenced by:

¶ ‣ §10.75(iii).

Encodings:

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T. Morita (1978)
Calculation of the complete elliptic integrals with complex modulus,

Numer. Math. 29 (2), pp. 233–236.

Notes:

An Algol procedure for calculating the complete elliptic integrals of the first and the second kind with complex modulus $k$ is included.

External Links:

ISSN 0029-599X, Document, MathReview (H. E. Fettis), ZentralBlatt.

Referenced by:

¶ ‣ §19.36(ii), §19.39(ii).

Encodings:

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J. Morris (1969)
Algorithm 346: F-test probabilities [S14],

Comm. ACM 12 (3), pp. 184–185.

Notes:

Includes Algol program, maximum accuracy 12S. For a remark see ACM Trans. Math. Software 14(1988), pp. 288-289

External Links:

ISSN 0001-0782, Document, Remark.

Referenced by:

§8.28(iv).

Encodings:

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R. Morris (1979)
The dilogarithm function of a real argument,

Math. Comp. 33 (146), pp. 778–787.

External Links:

ISSN 0025-5718, FullText, MathReview, ZentralBlatt.

Referenced by:

§25.19, §25.20.

Encodings:

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P. M. Morse and H. Feshbach (1953a)
Methods of Theoretical Physics,

Vol. 1, McGraw-Hill Book Co., New York.

Notes:

Reprinted by Feshbach Publishing, http://www.feshbachpublishing.com/.

External Links:

Feshbach Publishing, MathReview (M. Pinl), ZentralBlatt.

Referenced by:

¶ ‣ §1.17(iii), ¶ ‣ §1.5(ii), §12.17, §12.17, §12.17.

Encodings:

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P. M. Morse and H. Feshbach (1953b)
Methods of Theoretical Physics,

Vol. 2, McGraw-Hill Book Co., New York.

Notes:

Reprinted by Feshbach Publishing, http://www.feshbachpublishing.com/.

External Links:

Feshbach Publishing, MathReview (M. Pinl), ZentralBlatt.

Referenced by:

§12.17, §12.17.

Encodings:

BibTeX
C. Mortici (2011)
A new Stirling series as continued fraction,

Numer. Algorithms 56 (1), pp. 17–26.

External Links:

ISSN 1017-1398, Document, FullText, MathReview Entry, ZentralBlatt.

Referenced by:

§5.10, §5.10.

Encodings:

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L. Moser and M. Wyman (1958a)
Asymptotic development of the Stirling numbers of the first kind,

J. London Math. Soc. 33, pp. 133–146.

External Links:

Document, MathReview (N. J. Fine), ZentralBlatt.

Referenced by:

¶ ‣ §26.1, §26.8(vii).

Encodings:

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L. Moser and M. Wyman (1958b)
Stirling numbers of the second kind,

Duke Math. J. 25 (1), pp. 29–43.

External Links:

Document, MathReview (A. Sade), ZentralBlatt.

Referenced by:

¶ ‣ §26.1, §26.8(vii).

Encodings:

BibTeX
S. L. B. Moshier (1989)
Methods and Programs for Mathematical Functions,

Ellis Horwood Ltd., Chichester.

Notes:

Includes diskette

External Links:

ISBN 0-13-578998-2, MathReview, ZentralBlatt.

Referenced by:

§9.19(i), CEPHES (free C library).

Encodings:

BibTeX
N. F. Mott and H. S. W. Massey (1956)
Theory of Atomic Collisions,

3rd edition, Oxford Univ. Press., Oxford.

Notes:

Two-volume paperback version reprinted in 1987.

External Links:

ISBN 0-19-851242-2; (0-19-852030-1, 0-19-852031-X).

Referenced by:

§33.22(vi).

Encodings:

BibTeX
MPFR (free C library)

Notes:

MPFR is a C library for multiple-precision floating-point computations with correct rounding. The main goal of MPFR is to provide a library for multiple-precision floating-point computation which is both efficient and has well-defined semantics. MPFR includes most of the elementary functions. It also implements the gamma function, and more special functions are planned in the future.

External Links:

MPFR.

Referenced by:

§ ‣ § Software Cross Index.

Encodings:

BibTeX
mpmath (free python library)

Notes:

Mpmath is a pure-Python library for multiprecision floating-point arithmetic. It provides an extensive set of transcendental functions, unlimited exponent sizes, complex numbers, interval arithmetic, numerical integration and differentiation, root-finding, linear algebra, and much more.

External Links:

mpmath.

Referenced by:

§ ‣ § Software Cross Index.

Encodings:

BibTeX
R. J. Muirhead (1978)
Latent roots and matrix variates: A review of some asymptotic results,

Ann. Statist. 6 (1), pp. 5–33.

External Links:

FullText, MathReview (Yasuko Chikuse), ZentralBlatt.

Referenced by:

§35.6(i), §35.6(iii).

Encodings:

BibTeX
R. J. Muirhead (1982)
Aspects of Multivariate Statistical Theory,

John Wiley & Sons Inc., New York.

External Links:

ISBN 0-471-09442-0, MathReview (Nariaki Sugiura), ZentralBlatt.

Referenced by:

§35.11, §35.2, §35.4(i), §35.4(ii), §35.6(i), §35.6(ii), §35.7(i), §35.7(ii), §35.7(iii), §35.7(iv), ¶ ‣ §35.8(i), §35.8(ii), §35.8(iv), §35.9, Ch.35, Robb J. Muirhead.

Encodings:

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M. E. Muldoon and R. Spigler (1984)
Some remarks on zeros of cylinder functions,

SIAM J. Math. Anal. 15 (6), pp. 1231–1233.

External Links:

ISSN 0036-1410, Document, FullText, MathReview (A. K. Agarwal), ZentralBlatt.

Referenced by:

¶ ‣ §10.14, §10.21(ii).

Encodings:

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M. E. Muldoon (1970)
Singular integrals whose kernels involve certain Sturm-Liouville functions. I,

J. Math. Mech. 19 (10), pp. 855–873.

External Links:

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

Referenced by:

§9.10(ii).

Encodings:

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M. E. Muldoon (1977)
Higher monotonicity properties of certain Sturm-Liouville functions. V,

Proc. Roy. Soc. Edinburgh Sect. A 77 (1-2), pp. 23–37.

External Links:

MathReview (G. Sansone), ZentralBlatt.

Referenced by:

§10.21(ii), §9.11(iii).

Encodings:

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M. E. Muldoon (1979)
On the zeros of a cross-product of Bessel functions of different orders,

Z. Angew. Math. Mech. 59 (6), pp. 272–273.

External Links:

ISSN 0044-2267, Document, MathReview (F. W. J. Olver), ZentralBlatt.

Referenced by:

§10.21(x).

Encodings:

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M. E. Muldoon (1981)
The variation with respect to order of zeros of Bessel functions,

Rend. Sem. Mat. Univ. Politec. Torino 39 (2), pp. 15–25.

External Links:

MathReview (S. Ahmed), ZentralBlatt.

Referenced by:

§10.21(iv).

Encodings:

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H. P. Mulholland and S. Goldstein (1929)
The characteristic numbers of the Mathieu equation with purely imaginary parameter,

Phil. Mag. Series 7 8 (53), pp. 834–840.

External Links:

Document, ZentralBlatt.

Referenced by:

§28.7.

Encodings:

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J. Muller (1997)
Elementary Functions: Algorithms and Implementation,

Birkhäuser Boston Inc., Boston, MA.

Notes:

A 2nd edition was published in 2006.

External Links:

ISBN 0-8176-3990-X, MathReview (Warren E. Ferguson, Jr.), ZentralBlatt.

Referenced by:

¶ ‣ §4.45(i).

Encodings:

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D. Mumford (1983)
Tata Lectures on Theta. I,

Birkhäuser Boston Inc., Boston, MA.

External Links:

ISBN 3-7643-3109-7, Document, MathReview (M. Kh. Gizatullin), ZentralBlatt.

Referenced by:

§21.3(i), §21.3(ii), §21.5(i), §21.6(i), Ch.21.

Encodings:

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D. Mumford (1984)
Tata Lectures on Theta. II,

Birkhäuser Boston Inc., Boston, MA.

Notes:

Jacobian theta functions and differential equations

External Links:

ISBN 0-8176-3110-0, MathReview (M. Kh. Gizatullin), ZentralBlatt.

Referenced by:

§21.7(i), §21.7(ii), §21.7(iii), Ch.21.

Encodings:

BibTeX
MuPAD (commercial interactive system and Matlab toolbox)
SciFace Software, Paderborn, Germany.

Notes:

Computer algebra system for doing symbolic and exact algebraic computations as well as numerical calculations with almost arbitrary accuracy

Referenced by:

§ ‣ § Software Cross Index.

Encodings:

BibTeX
Y. Murata (1985)
Rational solutions of the second and the fourth Painlevé equations,

Funkcial. Ekvac. 28 (1), pp. 1–32.

External Links:

ISSN 0532-8721, FullText, MathReview (Hélène Airault), ZentralBlatt.

Referenced by:

§32.8(iv).

Encodings:

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Y. Murata (1995)
Classical solutions of the third Painlevé equation,

Nagoya Math. J. 139, pp. 37–65.

External Links:

ISSN 0027-7630, MathReview (Andrei A. Kapaev), ZentralBlatt.

Referenced by:

§32.8(iii).

Encodings:

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L. A. Muraveĭ (1976)
Zeros of the function ${\mathop{\mathrm{Ai}\/}\nolimits^{{\prime}}}(z)-\sigma\mathop{\mathrm{Ai}\/}\nolimits(z)$ ,

Differential Equations 11, pp. 797–811.

External Links:

ZentralBlatt.

Referenced by:

§9.9(i).

Encodings:

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B. T. M. Murphy and A. D. Wood (1997)
Hyperasymptotic solutions of second-order ordinary differential equations with a singularity of arbitrary integer rank,

Methods Appl. Anal. 4 (3), pp. 250–260.

External Links:

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

Referenced by:

§2.11(v).

Encodings:

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J. Murzewski and A. Sowa (1972)
Tables of the functions of the parabolic cylinder for negative integer parameters,

Zastos. Mat. 13, pp. 261–273.

External Links:

MathReview, ZentralBlatt.

Referenced by:

§12.19.

Encodings:

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L. Mutafchiev and E. Kamenov (2006)
Asymptotic formula for the number of plane partitions of positive integers,

C. R. Acad. Bulgare Sci. 59 (4), pp. 361–366.

External Links:

ISSN 1310-1331, FullText, MathReview Entry, ZentralBlatt.

Referenced by:

§26.12(iv).

Encodings:

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D. Müller, B. G. Kelly and J. J. O’Brien (1994)
Spheroidal eigenfunctions of the tidal equation,

Phys. Rev. Lett. 73 (11), pp. 1557–1560.

External Links:

ISSN 0031-9007, Document, MathReview, ZentralBlatt.

Referenced by:

§30.13(v).

Encodings:

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H. J. W. Müller (1962)
Asymptotic expansions of oblate spheroidal wave functions and their characteristic numbers,

J. Reine Angew. Math. 211, pp. 33–47.

External Links:

MathReview (J. Meixner), ZentralBlatt.

Referenced by:

§30.9(ii), §30.9(ii).

Encodings:

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H. J. W. Müller (1963)
Asymptotic expansions of prolate spheroidal wave functions and their characteristic numbers,

J. Reine Angew. Math. 212, pp. 26–48.

External Links:

MathReview (J. Meixner), ZentralBlatt.

Referenced by:

§30.9(i), §30.9(i).

Encodings:

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H. J. W. Müller (1966a)
Asymptotic expansions of ellipsoidal wave functions and their characteristic numbers,

Math. Nachr. 31, pp. 89–101.

External Links:

Document, MathReview (F. M. Arscott), ZentralBlatt.

Referenced by:

§29.11, §29.7(i), §29.7(ii).

Encodings:

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H. J. W. Müller (1966b)
Asymptotic expansions of ellipsoidal wave functions in terms of Hermite functions,

Math. Nachr. 32, pp. 49–62.

External Links:

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

Referenced by:

§29.11, §29.7(ii).

Encodings:

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H. J. W. Müller (1966c)
On asymptotic expansions of ellipsoidal wave functions,

Math. Nachr. 32, pp. 157–172.

External Links:

Document, MathReview (F. M. Arscott), ZentralBlatt.

Referenced by:

§29.11, §29.7(ii).

Encodings:

BibTeX
K. H. Müller (1988)
Elastodynamics in parabolic cylinders,

Z. Angew. Math. Phys. 39 (5), pp. 748–752.

External Links:

ISSN 0044-2275, Document, MathReview (Sergej M. Zverev).

Referenced by:

§12.17.

Encodings:

BibTeX