Bibliography L

♦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♦

G. Labahn and M. Mutrie (1997)
Reduction of Elliptic Integrals to Legendre Normal Form,

Technical report

Technical Report 97-21, Department of Computer Science, University of Waterloo, Waterloo, Ontario.

Referenced by:

§19.14(ii).

Encodings:

BibTeX
A. Laforgia and M. E. Muldoon (1983)
Inequalities and approximations for zeros of Bessel functions of small order,

SIAM J. Math. Anal. 14 (2), pp. 383–388.

External Links:

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

Referenced by:

§10.21(iv).

Encodings:

BibTeX
A. Laforgia and M. E. Muldoon (1988)
Monotonicity properties of zeros of generalized Airy functions,

Z. Angew. Math. Phys. 39 (2), pp. 267–271.

External Links:

ISSN 0044-2275, Document, MathReview (Evangelos Ifantis), ZentralBlatt.

Referenced by:

§9.13(i).

Encodings:

BibTeX
A. Laforgia and S. Sismondi (1988)
Monotonicity results and inequalities for the gamma and error functions,

J. Comput. Appl. Math. 23 (1), pp. 25–33.

External Links:

ISSN 0377-0427, Document, MathReview (M. E. Cohen), ZentralBlatt.

Referenced by:

§7.8.

Encodings:

BibTeX
A. Laforgia (1979)
On the Zeros of the Derivative of Bessel Functions of Second Kind,

Pubblicazioni Serie III [Publication Series III], Vol. 179, Istituto per le Applicazioni del Calcolo “Mauro Picone” (IAC), Rome.

External Links:

MathReview.

Referenced by:

§10.21(vi).

Encodings:

BibTeX
A. Laforgia (1984)
Further inequalities for the gamma function,

Math. Comp. 42 (166), pp. 597–600.

External Links:

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

Referenced by:

§5.6(i).

Encodings:

BibTeX
A. Laforgia (1986)
Inequalities for Bessel functions,

J. Comput. Appl. Math. 15 (1), pp. 75–81.

External Links:

ISSN 0377-0427, Document, MathReview (B. D. Agrawal), ZentralBlatt.

Referenced by:

§10.14.

Encodings:

BibTeX
A. Laforgia (1991)
Bounds for modified Bessel functions,

J. Comput. Appl. Math. 34 (3), pp. 263–267.

External Links:

ISSN 0377-0427, Document, MathReview (N. Hayek Calil), ZentralBlatt.

Referenced by:

§10.37.

Encodings:

BibTeX
J. C. Lagarias, V. S. Miller and A. M. Odlyzko (1985)
Computing $\pi(x)$ : The Meissel-Lehmer method,

Math. Comp. 44 (170), pp. 537–560.

External Links:

ISSN 0025-5718, FullText, MathReview (Kenneth A. Jukes), ZentralBlatt.

Referenced by:

§27.18.

Encodings:

BibTeX
J. Lagrange (1770)
Démonstration d’un Théoréme d’Arithmétique,

Nouveau Mém. Acad. Roy. Sci. Berlin, pp. 123–133 (French).

Notes:

Reprinted in Oeuvres, Vol. 3, pp. 189–201, Gauthier-Villars, Paris, 1867

External Links:

FullText.

Referenced by:

§27.13(iii).

Encodings:

BibTeX
S. Lai and Y. Chiu (1990)
Exact computation of the 3- $j$ and 6- $j$ symbols,

Comput. Phys. Comm. 61 (3), pp. 350–360.

Notes:

A Fortran program is included.

External Links:

Document, ZentralBlatt.

Referenced by:

§34.15.

Encodings:

BibTeX
S. Lai and Y. Chiu (1992)
Exact computation of the 9- $j$ symbols,

Comput. Phys. Comm. 70 (3), pp. 544–556.

Notes:

Double-precision Fortran

External Links:

ISSN 0010-4655, Document, Code, MathReview.

Referenced by:

§34.15.

Encodings:

BibTeX
H. Lamb (1932)
Hydrodynamics,

6th edition, Cambridge University Press, Cambridge.

Notes:

Reprinted in 1993.

External Links:

ISBN 0-521-45868-4, Document, MathReview, ZentralBlatt.

Referenced by:

§10.73(i).

Encodings:

BibTeX
C. G. Lambe and D. R. Ward (1934)
Some differential equations and associated integral equations,

Quart. J. Math. (Oxford) 5, pp. 81–97.

External Links:

Document, ZentralBlatt.

Referenced by:

§31.10(i), §31.9(i).

Encodings:

BibTeX
C. G. Lambe (1952)
Lamé-Wangerin functions,

Quart. J. Math., Oxford Ser. (2) 3, pp. 107–114.

External Links:

Document, MathReview (A. Erdélyi), ZentralBlatt.

Referenced by:

§29.17(ii).

Encodings:

BibTeX
E. Landau (1953)
Handbuch der Lehre von der Verteilung der Primzahlen. 2 Bände,

Chelsea Publishing Co., New York (German).

Notes:

2nd edition, with an appendix by Paul T. Bateman

External Links:

MathReview (L. Schoenfeld), ZentralBlatt.

Referenced by:

§25.8.

Encodings:

BibTeX
L. D. Landau and E. M. Lifshitz (1962)
The Classical Theory of Fields,

Pergamon Press, Oxford.

Notes:

Revised second edition. Course of Theoretical Physics, Vol. 2. Translated from the Russian by Morton Hamermesh

External Links:

MathReview (E. L. Hill), ZentralBlatt.

Referenced by:

§9.16.

Encodings:

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L. D. Landau and E. M. Lifshitz (1965)
Quantum Mechanics: Non-relativistic Theory,

Pergamon Press Ltd., Oxford.

Notes:

Revised second edition. Course of Theoretical Physics, Vol. 3. Translated from the Russian by J. B. Sykes and J. S. Bell

External Links:

MathReview, ZentralBlatt.

Referenced by:

§9.16.

Encodings:

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L. D. Landau and E. M. Lifshitz (1987)
Fluid Mechanics,

2nd edition, Pergamon Press, London.

Notes:

Course of Theoretical Physics, Vol. 6. Translated from the Russian by J. B. Sykes and W. H. Reid

External Links:

ISBN 0-7506-2767-0;0-08-033932-8, MathReview, ZentralBlatt.

Referenced by:

§9.16.

Encodings:

BibTeX
L. J. Landau (1999)
Ratios of Bessel functions and roots of $\alpha J_{\nu}(x)+xJ^{{\prime}}_{\nu}(x)=0$ ,

J. Math. Anal. Appl. 240 (1), pp. 174–204.

External Links:

ISSN 0022-247X, Document, MathReview (Boro Döring), ZentralBlatt.

Referenced by:

¶ ‣ §10.14, ¶ ‣ §10.15, §10.21(xii).

Encodings:

BibTeX
L. J. Landau (2000)
Bessel functions: Monotonicity and bounds,

J. London Math. Soc. (2) 61 (1), pp. 197–215.

External Links:

ISSN 0024-6107, Document, MathReview (M. E. Muldoon), ZentralBlatt.

Referenced by:

¶ ‣ §10.14, ¶ ‣ §10.15.

Encodings:

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S. Lang (1987)
Elliptic Functions,

2nd edition, Graduate Texts in Mathematics, Vol. 112, Springer-Verlag, New York.

Notes:

With an appendix by J. Tate

External Links:

ISBN 0-387-96508-4, MathReview, ZentralBlatt.

Referenced by:

§22.18(iv).

Encodings:

BibTeX
R. E. Langer (1934)
The solutions of the Mathieu equation with a complex variable and at least one parameter large,

Trans. Amer. Math. Soc. 36 (3), pp. 637–695.

External Links:

ISSN 0002-9947, FullText, MathReview Entry, ZentralBlatt.

Referenced by:

¶ ‣ §28.8(iv).

Encodings:

BibTeX
L. Lapointe and L. Vinet (1996)
Exact operator solution of the Calogero-Sutherland model,

Comm. Math. Phys. 178 (2), pp. 425–452.

Notes:

For a Maple implementation of the algorithm given in this paper for Jack and zonal polynomials see Zeilberger (Web Site).

External Links:

ISSN 0010-3616, Link, MathReview (Kazuhiro Hikami), ZentralBlatt.

Referenced by:

§35.12.

Encodings:

BibTeX
T. M. Larsen, D. Erricolo and P. L. E. Uslenghi (2009)
New method to obtain small parameter power series expansions of Mathieu radial and angular functions,

Math. Comp. 78 (265), pp. 255–274.

External Links:

ISSN 0025-5718, Document, FullText, MathReview (Junesang Choi), ZentralBlatt.

Referenced by:

§28.24, §28.24.

Encodings:

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H. T. Lau (1995)
A Numerical Library in C for Scientists and Engineers,

CRC Press, Boca Raton, FL.

Notes:

With 1 IBM-PC floppy disk (3.5 inch; HD) containing a large general purpose mathematical software collection written in C including a collection of special function classes. The functions are computed for real variables only. (See Lau (2004) for Java version).

External Links:

ISBN 0-8493-7376-X, MathReview, ZentralBlatt.

Referenced by:

§ ‣ § Software Cross Index, H. T. Lau (2004).

Encodings:

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H. T. Lau (2004)
A Numerical Library in Java for Scientists & Engineers,

Chapman & Hall/CRC, Boca Raton, FL.

Notes:

With 1 CD-ROM (Windows, Macintosh and Unix) containing a large general purpose mathematical software collection written in Java including a collection of special function classes. The functions are computed for real variables only. (See Lau (1995) for C version).

External Links:

ISBN 1-58488-430-4, MathReview Entry, ZentralBlatt.

Referenced by:

H. T. Lau (1995).

Encodings:

BibTeX
B. J. Laurenzi (1993)
Moment integrals of powers of Airy functions,

Z. Angew. Math. Phys. 44 (5), pp. 891–908.

External Links:

ISSN 0044-2275, Document, MathReview (B. M. Agrawal), ZentralBlatt.

Referenced by:

§9.11(v), §9.11(v).

Encodings:

BibTeX
H. A. Lauwerier (1974)
Asymptotic Analysis,

Mathematical Centre Tracts, Mathematisch Centrum, Amsterdam.

External Links:

MathReview (C. Comstock), ZentralBlatt.

Referenced by:

Ch.2.

Encodings:

BibTeX
D. F. Lawden (1989)
Elliptic Functions and Applications,

Applied Mathematical Sciences, Vol. 80, Springer-Verlag, New York.

External Links:

ISBN 0-387-96965-9, MathReview (Bruce C. Berndt), ZentralBlatt.

Referenced by:

§19.36(iii), §20.13, §20.15, §20.2(i), §20.2(ii), §20.2(iii), §20.2(iv), §20.4(i), §20.5(i), §20.5(ii), §20.7(i), §20.7(ii), §20.7(iv), §20.7(vi), §20.7(vii), §20.7(vii), §20.7(viii), Ch.20, §22.10(i), §22.10(ii), §22.12, §22.13(i), §22.14(i), §22.14(ii), §22.14(iii), §22.14(iii), §22.15(i), §22.15(ii), §22.15(ii), §22.16(ii), §22.16(iii), §22.17(i), ¶ ‣ §22.18(i), §22.18(iii), ¶ ‣ §22.19(ii), §22.19(i), §22.19(i), §22.19(ii), §22.19(ii), §22.19(iv), §22.19(v), §22.2, §22.20(vii), §22.21, §22.4(i), §22.4(iii), §22.5(i), §22.5(ii), §22.6(ii), §22.6(iii), §22.6(iv), §22.7(i), §22.7(ii), §22.8(i), §22.8(ii), Ch.22, §23.10(i), §23.10(i), §23.10(iii), §23.10(iv), §23.12, §23.2(ii), §23.2(iii), §23.2(iii), §23.21(i), §23.3(i), §23.3(ii), ¶ ‣ §23.6(iv), §23.6(i), §23.6(i), §23.6(ii), §23.6(ii), §23.6(iii), §23.7, §23.8(i), §23.8(ii), §23.8(iii), Ch.23.

Encodings:

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W. Lay, K. Bay and S. Yu. Slavyanov (1998)
Asymptotic and numeric study of eigenvalues of the double confluent Heun equation,

J. Phys. A 31 (42), pp. 8521–8531.

External Links:

ISSN 0305-4470, Document, MathReview, ZentralBlatt.

Referenced by:

§31.13, §31.18.

Encodings:

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W. Lay and S. Yu. Slavyanov (1998)
The central two-point connection problem for the Heun class of ODEs,

J. Phys. A 31 (18), pp. 4249–4261.

External Links:

ISSN 0305-4470, Document, MathReview, ZentralBlatt.

Referenced by:

¶ ‣ §31.12.

Encodings:

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W. Lay and S. Yu. Slavyanov (1999)
Heun’s equation with nearby singularities,

Proc. Roy. Soc. London Ser. A 455, pp. 4347–4361.

External Links:

ISSN 1364-5021, Document, MathReview, ZentralBlatt.

Referenced by:

§31.13, §31.17(ii).

Encodings:

BibTeX
V. Laĭ (1994)
The two-point connection problem for differential equations of the Heun class,

Teoret. Mat. Fiz. 101 (3), pp. 360–368 (Russian).

Notes:

In Russian. English translation: Theoret. and Math. Phys. 101(1994), no. 3, pp. 1413–1418 (1995)

External Links:

ISSN 0564-6162, Document, MathReview, ZentralBlatt.

Referenced by:

§31.18.

Encodings:

BibTeX
D. Le (1985)
An efficient derivative-free method for solving nonlinear equations,

ACM Trans. Math. Software 11 (3), pp. 250–262.

Notes:

Corrigendum, ibid. 15(3) (1989), 287

External Links:

ISSN 0098-3500, Document, MathReview (T. Feagin), ZentralBlatt.

Referenced by:

¶ ‣ §3.8(iii).

Encodings:

BibTeX
E. W. Leaver (1986)
Solutions to a generalized spheroidal wave equation: Teukolsky’s equations in general relativity, and the two-center problem in molecular quantum mechanics,

J. Math. Phys. 27 (5), pp. 1238–1265.

External Links:

ISSN 0022-2488, Document, MathReview (Basilis C. Xanthopoulos), ZentralBlatt.

Referenced by:

§30.12, §31.17(ii).

Encodings:

BibTeX
A. V. Lebedev and R. M. Fedorova (1960)
A Guide to Mathematical Tables,

Pergamon Press, Amsterdam-New York-Oxford.

Notes:

See also Burunova (1960).

External Links:

MathReview, ZentralBlatt.

Referenced by:

§10.75(i), §11.14(i), §12.19, §13.30, §14.33, §18.41(iii), §19.37(i), §20.15, §22.21, §23.23, §24.20, §28.35(iv), §4.46, §5.22(i), §6.19(i), §7.23(i), §8.26(i), §9.18(i).

Encodings:

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N. N. Lebedev, I. P. Skalskaya and Y. S. Uflyand (1965)
Problems of Mathematical Physics,

Revised, enlarged and corrected English edition; translated and edited by Richard A. Silverman. With a supplement by Edward L. Reiss, Prentice-Hall Inc., Englewood Cliffs, NJ.

Notes:

Republished as Worked Problems in Applied Mathematics by Dover Publications, New York, 1979

External Links:

ISBN 0-486-63730-1, MathReview (J. Mathews), ZentralBlatt.

Referenced by:

§10.43(v).

Encodings:

BibTeX
N. N. Lebedev (1965)
Special Functions and Their Applications,

Prentice-Hall Inc., Englewood Cliffs, N.J..

Notes:

R. A. Silverman, translator and editor; reprinted by Dover, New York, 1972.

External Links:

MathReview (A. Erdélyi), ZentralBlatt.

Referenced by:

Ch.12, §18.18(i), §6.17, §6.7(i), Ch.6, Ch.7, §9.11(iii), Ch.9.

Encodings:

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J. LeCaine (1945)
A table of integrals involving the functions $E_{n}(x)$ ,

Notes:

National Research Council of Canada, Division of Atomic Energy, Document no. MT-131 (NRC 1553)

Referenced by:

§8.19(x).

Encodings:

BibTeX
D. K. Lee (1990)
Application of theta functions for numerical evaluation of complete elliptic integrals of the first and second kinds,

Comput. Phys. Comm. 60 (3), pp. 319–327.

External Links:

ISSN 0010-4655, Document, MathReview, ZentralBlatt.

Referenced by:

§19.36(iii), §19.5.

Encodings:

BibTeX
Soo-Y. Lee (1980)
The inhomogeneous Airy functions, $\mathop{\mathrm{Gi}\/}\nolimits(z)$ and $\mathop{\mathrm{Hi}\/}\nolimits(z)$ ,

J. Chem. Phys. 72 (1), pp. 332–336.

External Links:

ISSN 0021-9606, Document, MathReview (V. L. Deshpande).

Referenced by:

§9.12(vii), §9.17(iii).

Encodings:

BibTeX
W. R. Leeb (1979)
Algorithm 537: Characteristic values of Mathieu’s differential equation,

ACM Trans. Math. Software 5 (1), pp. 112–117.

External Links:

ISSN 0098-3500, Document, TOMS module 537 (in GAMS).

Referenced by:

§28.36(ii), §28.36(iii).

Encodings:

BibTeX
D. J. Leeming (1977)
An asymptotic estimate for the Bernoulli and Euler numbers,

Canad. Math. Bull. 20 (1), pp. 109–111.

External Links:

MathReview (D. H. Lehmer), ZentralBlatt.

Referenced by:

§24.11.

Encodings:

BibTeX
D. J. Leeming (1989)
The real zeros of the Bernoulli polynomials,

J. Approx. Theory 58 (2), pp. 124–150.

External Links:

ISSN 0021-9045, Document, MathReview (Boro Döring), ZentralBlatt.

Referenced by:

§24.12(i), §24.9.

Encodings:

BibTeX
A. M. Legendre (1808)
Essai sur la Théorie des Nombres,

2nd edition, Courcier, Paris.

Referenced by:

§27.2(i).

Encodings:

BibTeX
A. M. Legendre (1825)
Traité des fonctions elliptiques et des intégrales Eulériennes,

Huzard-Courcier, Paris.

Notes:

vol.1, 1825; vol.2, 1826; three supplements, 1828–1832.

Referenced by:

§19.14(ii), Ch.19.

Encodings:

BibTeX
D. R. Lehman and J. S. O’Connell (1973)
Graphical Recoupling of Angular Momenta,

Technical report

U.S. Government Printing Office, National Bureau of Standards, Washington, D.C..

Notes:

Monograph 136

Referenced by:

§34.9.

Encodings:

BibTeX
D. R. Lehman, W. C. Parke and L. C. Maximon (1981)
Numerical evaluation of integrals containing a spherical Bessel function by product integration,

J. Math. Phys. 22 (7), pp. 1399–1413.

External Links:

ISSN 0022-2488, Document, MathReview (C. W. Clenshaw), ZentralBlatt.

Referenced by:

¶ ‣ §10.74(vii).

Encodings:

BibTeX
D. H. Lehmer (1943)
Ramanujan’s function $\mathop{\tau\/}\nolimits(n)$ ,

Duke Math. J. 10 (3), pp. 483–492.

External Links:

Document, MathReview (H. S. Zuckerman), ZentralBlatt.

Referenced by:

§27.20, §27.21.

Encodings:

BibTeX
D. H. Lehmer (1947)
The vanishing of Ramanujan’s function $\mathop{\tau\/}\nolimits(n)$ ,

Duke Math. J. 14 (2), pp. 429–433.

External Links:

Document, MathReview (R. A. Rankin), ZentralBlatt.

Referenced by:

§27.14(vi).

Encodings:

BibTeX
D. H. Lehmer (1940)
On the maxima and minima of Bernoulli polynomials,

Amer. Math. Monthly 47 (8), pp. 533–538.

External Links:

FullText, MathReview (W. E. Milne), ZentralBlatt.

Referenced by:

§24.12(i), §24.9.

Encodings:

BibTeX
D. H. Lehmer (1941)
Guide to Tables in the Theory of Numbers,

Bulletin of the National Research Council, No. 105, National Research Council, Washington, D. C..

Notes:

Reprinted in 1961.

External Links:

MathReview (R. D. Carmichael), ZentralBlatt.

Referenced by:

§27.20, §27.21, §27.21.

Encodings:

BibTeX
D. N. Lehmer (1914)
List of Prime Numbers from 1 to 10,006,721,

Publ. No. 165, Carnegie Institution of Washington, Washington, DC.

Referenced by:

§27.21.

Encodings:

BibTeX
J. Lehner (1941)
A partition function connected with the modulus five,

Duke Math. J. 8 (4), pp. 631–655.

External Links:

Document, MathReview (R. D. James), ZentralBlatt.

Referenced by:

§17.18.

Encodings:

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O. Lehto and K. I. Virtanen (1973)
Quasiconformal Mappings in the Plane,

2nd edition, Springer-Verlag, New York.

Notes:

Translated from the German by K. W. Lucas, Die Grundlehren der mathematischen Wissenschaften, Band 126

External Links:

MathReview, ZentralBlatt.

Referenced by:

§19.9(i).

Encodings:

BibTeX
A. Leitner and J. Meixner (1960)
Eine Verallgemeinerung der Sphäroidfunktionen,

Arch. Math. 11, pp. 29–39.

External Links:

ISSN 0003-9268, Document, MathReview (M. J. O. Strutt), ZentralBlatt.

Referenced by:

§30.12.

Encodings:

BibTeX
D. Lemoine (1997)
Optimal cylindrical and spherical Bessel transforms satisfying bound state boundary conditions,

Comput. Phys. Comm. 99 (2-3), pp. 297–306.

Notes:

Single-precision Fortran, maximum accuracy 8S.

External Links:

ISSN 0010-4655, Document, Code, ZentralBlatt.

Referenced by:

§10.77(ix).

Encodings:

BibTeX
D. A. Leonard (1982)
Orthogonal polynomials, duality and association schemes,

SIAM J. Math. Anal. 13 (4), pp. 656–663.

External Links:

ISSN 0036-1410, Document, MathReview (C. L. Parihar), ZentralBlatt.

Referenced by:

¶ ‣ §18.38(iii).

Encodings:

BibTeX
N. L. Lepe (1985)
Functions on a parabolic cylinder with a negative integer index,

Differ. Uravn. 21 (11), pp. 2001–2003, 2024 (Russian).

Notes:

In Russian.

External Links:

ISSN 0374-0641, MathReview, ZentralBlatt.

Referenced by:

§12.13(i).

Encodings:

BibTeX
J. Lepowsky and S. Milne (1978)
Lie algebraic approaches to classical partition identities,

Adv. in Math. 29 (1), pp. 15–59.

External Links:

ISSN 0001-8708, Document, MathReview (S. I. Gel’fand), ZentralBlatt.

Referenced by:

§17.16.

Encodings:

BibTeX
J. Lepowsky and R. L. Wilson (1982)
A Lie theoretic interpretation and proof of the Rogers-Ramanujan identities,

Adv. in Math. 45 (1), pp. 21–72.

External Links:

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

Referenced by:

§17.16.

Encodings:

BibTeX
M. Lerch (1887)
Note sur la fonction $\mathfrak{K}(w,x,s)=\sum _{{k=0}}^{\infty}\frac{e^{{2k\pi ix}}}{(w+k)^{s}}$ ,

Acta Math. 11 (1-4), pp. 19–24 (French).

External Links:

ISSN 0001-5962, Document, MathReview Entry, ZentralBlatt.

Referenced by:

§25.14(i).

Encodings:

BibTeX
M. Lerch (1903)
Zur Theorie der Gaußschen Summen,

Math. Ann. 57 (4), pp. 554–567 (German).

External Links:

ISSN 0025-5831, Document, MathReview Entry, ZentralBlatt.

Referenced by:

§20.11(i).

Encodings:

BibTeX
J. Letessier, G. Valent and J. Wimp (1994)
Some Differential Equations Satisfied by Hypergeometric Functions,

in Approximation and Computation (West Lafayette, IN, 1993),

Internat. Ser. Numer. Math., Vol. 119, pp. 371–381.

External Links:

MathReview (M. E. Muldoon), ZentralBlatt.

Referenced by:

§16.8(ii).

Encodings:

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J. Letessier (1995)
Co-recursive associated Jacobi polynomials,

J. Comput. Appl. Math. 57 (1-2), pp. 203–213.

External Links:

ISSN 0377-0427, Document, MathReview, ZentralBlatt.

Referenced by:

¶ ‣ §18.30.

Encodings:

BibTeX
C. Leubner and H. Ritsch (1986)
A note on the uniform asymptotic expansion of integrals with coalescing endpoint and saddle points,

J. Phys. A 19 (3), pp. 329–335.

External Links:

ISSN 0305-4470, Document, MathReview (F. W. J. Olver), ZentralBlatt.

Referenced by:

§2.4(vi).

Encodings:

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K. V. Leung and S. S. Ghaderpanah (1979)
An application of the finite element approximation method to find the complex zeros of the modified Bessel function $K_{{n}}(z)$ ,

Math. Comp. 33 (148), pp. 1299–1306.

External Links:

ISSN 0025-5718, FullText, MathReview (R. P. Boas, Jr.), ZentralBlatt.

Referenced by:

¶ ‣ §10.74(vi), §10.75(vi).

Encodings:

BibTeX
L. Levey and L. B. Felsen (1969)
On incomplete Airy functions and their application to diffraction problems,

Radio Sci. 4 (10), pp. 959–969.

External Links:

ISSN 0048-6604, Document, MathReview (T. Erber).

Referenced by:

§9.14.

Encodings:

BibTeX
E. Levin and D. S. Lubinsky (2001)
Orthogonal Polynomials for Exponential Weights,

CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC, 4, Springer-Verlag, New York.

External Links:

ISBN 0-387-98941-2, MathReview (Walter Van Assche), ZentralBlatt.

Referenced by:

§18.32.

Encodings:

BibTeX
D. A. Levine (1969)
Algorithm 344: Student’s t-distribution [S14],

Comm. ACM 12 (1), pp. 37–38.

Notes:

Single-precision Fortran, maximum accuracy 8S. For Remarks see same journal 13(1970), pp. 124 and 449.

External Links:

ISSN 0001-0782, Document, Remark 1 and Remark 2.

Referenced by:

§8.28(iv).

Encodings:

BibTeX
H. Levine and J. Schwinger (1948)
On the theory of diffraction by an aperture in an infinite plane screen. I,

Phys. Rev. 74 (8), pp. 958–974.

External Links:

Document, MathReview (C. J. Bouwkamp), ZentralBlatt.

Referenced by:

§11.12.

Encodings:

BibTeX
N. Levinson and R. M. Redheffer (1970)
Complex Variables,

Holden-Day Inc., San Francisco, CA.

External Links:

MathReview (J. E. Miller), ZentralBlatt.

Referenced by:

§1.10(i), §1.10(x), §1.10(ii), §1.10(iii), §1.10(vi), §1.9(i), §1.9(ii), §1.9(iii), §1.9(iv), §1.9(vi), §4.14, §4.2(i), §4.2(iv), §4.20, §4.22, §4.23(ii), §4.23(v), §4.24(ii), §4.28, §4.31, §4.37(ii), §4.4(i), §4.4(ii), §4.7(i), §4.7(ii), §4.8(i), Ch.4.

Encodings:

BibTeX
N. Levinson (1974)
More than one third of zeros of Riemann’s zeta-function are on $\sigma=\frac{1}{2}$ ,

Advances in Math. 13 (4), pp. 383–436.

External Links:

Document, MathReview (H. L. Montgomery), ZentralBlatt.

Referenced by:

§25.10(ii).

Encodings:

BibTeX
J. S. Lew (1994)
On the Darling-Mandelbrot probability density and the zeros of some incomplete gamma functions,

Constr. Approx. 10 (1), pp. 15–30.

External Links:

ISSN 0176-4276, Document, MathReview (P. Anandani), ZentralBlatt.

Referenced by:

§8.13(i).

Encodings:

BibTeX
S. Lewanowicz (1985)
Recurrence relations for hypergeometric functions of unit argument,

Math. Comp. 45 (172), pp. 521–535.

External Links:

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

Referenced by:

§16.4(iii).

Encodings:

BibTeX
S. Lewanowicz (1987)
Corrigenda: “Recurrence relations for hypergeometric functions of unit argument” [Math. Comp. 45 (1985), no. 172, 521–535; MR 86m:33004],

Math. Comp. 48 (178), pp. 853.

External Links:

ISSN 0025-5718, FullText, MathReview, ZentralBlatt.

Referenced by:

§16.4(iii).

Encodings:

BibTeX
S. Lewanowicz (1991)
Evaluation of Bessel function integrals with algebraic singularities,

J. Comput. Appl. Math. 37 (1-3), pp. 101–112.

External Links:

ISSN 0377-0427, Document, MathReview, ZentralBlatt.

Referenced by:

¶ ‣ §10.74(vii).

Encodings:

BibTeX
L. Lewin (1981)
Polylogarithms and Associated Functions,

North-Holland Publishing Co., New York.

Notes:

With a foreword by A. J. Van der Poorten

External Links:

ISBN 0-444-00550-1, MathReview, ZentralBlatt.

Referenced by:

¶ ‣ §25.12(ii), §25.12(i), §25.12(i).

Encodings:

BibTeX
J. T. Lewis and M. E. Muldoon (1977)
Monotonicity and convexity properties of zeros of Bessel functions,

SIAM J. Math. Anal. 8 (1), pp. 171–178.

External Links:

ISSN 1095-7154, Document, MathReview (T. Erber), ZentralBlatt.

Referenced by:

§10.21(iv).

Encodings:

BibTeX
L.-W. Li, M. Leong, T.-S. Yeo, P.-S. Kooi and K.-Y. Tan (1998a)
Computations of spheroidal harmonics with complex arguments: A review with an algorithm,

Phys. Rev. E 58 (5), pp. 6792–6806.

Notes:

Mathematica package for eigenvalues and solutions of the spheroidal wave equations

External Links:

Code(SpheroidF), Document.

Referenced by:

§30.18(ii), §30.18(iii).

Encodings:

BibTeX
L.-W. Li, T. S. Yeo, P. S. Kooi and M. S. Leong (1998b)
Microwave specific attenuation by oblate spheroidal raindrops: An exact analysis of TCS’s in terms of spheroidal wave functions,

J. Electromagn. Waves Appl. 12 (6), pp. 709–711.

External Links:

ISSN 0920-5071, Document, MathReview.

Referenced by:

§30.14(v).

Encodings:

BibTeX

X. Li and R. Wong (1994)
Error bounds for asymptotic expansions of Laplace convolutions,

SIAM J. Math. Anal. 25 (6), pp. 1537–1553.

External Links:

ISSN 0036-1410, Document, MathReview (Walter Schempp), ZentralBlatt.

Referenced by:

¶ ‣ §2.6(iii).

Encodings:

BibTeX
X. Li and R. Wong (2000)
A uniform asymptotic expansion for Krawtchouk polynomials,

J. Approx. Theory 106 (1), pp. 155–184.

External Links:

ISSN 0021-9045, Document, MathReview (Ahmed I. Zayed), ZentralBlatt.

Referenced by:

¶ ‣ §18.24.

Encodings:

BibTeX
X. Li and R. Wong (2001)
On the asymptotics of the Meixner-Pollaczek polynomials and their zeros,

Constr. Approx. 17 (1), pp. 59–90.

External Links:

ISSN 0176-4276, Document, MathReview (C. M. Joshi), ZentralBlatt.

Referenced by:

¶ ‣ §18.24.

Encodings:

BibTeX
X. Li, X. Shi and J. Zhang (1991)
Generalized Riemann $\zeta{}$ -function regularization and Casimir energy for a piecewise uniform string,

Phys. Rev. D 44 (2), pp. 560–562.

External Links:

Document.

Referenced by:

§24.18.

Encodings:

BibTeX
Y. T. Li and R. Wong (2008)
Integral and series representations of the Dirac delta function,

Commun. Pure Appl. Anal. 7 (2), pp. 229–247.

External Links:

ISSN 1534-0392, MathReview Entry, ZentralBlatt.

Referenced by:

§1.17(iv).

Encodings:

BibTeX
Y. A. Li and P. J. Olver (2000)
Well-posedness and blow-up solutions for an integrable nonlinearly dispersive model wave equation,

J. Differential Equations 162 (1), pp. 27–63.

External Links:

ISSN 0022-0396, Document, MathReview (John Albert), ZentralBlatt.

Referenced by:

§22.19(iii).

Encodings:

BibTeX
E. M. Lifshitz and L. P. Pitaevskiĭ (1980)
Statistical Physics, Part 2: Theory of the Condensed State,

Pergamon Press, Oxford.

Notes:

Course of Theoretical Physics , Vol. 9. Translated from the Russian by J. B. Sykes and M. J. Kearsley.

External Links:

ISBN 0-08-023073-3; 0-08-023072-5, MathReview.

Referenced by:

§25.17.

Encodings:

BibTeX
M. J. Lighthill (1958)
An Introduction to Fourier Analysis and Generalised Functions,

Cambridge Monographs on Mechanics and Applied Mathematics, Cambridge University Press, New York.

External Links:

ISBN 0521091284, MathReview (G. Temple), ZentralBlatt.

Referenced by:

§1.16(v).

Encodings:

BibTeX
E. Lindelöf (1905)
Le Calcul des Résidus et ses Applications à la Théorie des Fonctions,

Gauthier-Villars, Paris (French).

Notes:

Reprinted by Éditions Jacques Gabay, Sceaux, 1989.

External Links:

ISBN 2-87647-060-8, MathReview, ZentralBlatt.

Referenced by:

§25.11(vii), §25.5(i).

Encodings:

BibTeX
P. Linz and T. E. Kropp (1973)
A note on the computation of integrals involving products of trigonometric and Bessel functions,

Math. Comp. 27 (124), pp. 871–872.

External Links:

ISSN 0025-5718, FullText, Document, MathReview, ZentralBlatt.

Referenced by:

¶ ‣ §10.74(vii).

Encodings:

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J. E. Littlewood (1914)
Sur la distribution des nombres premiers,

Comptes Rendus de l’Academie des Sciences, Paris 158, pp. 1869–1872 (French).

External Links:

ZentralBlatt.

Referenced by:

¶ ‣ §27.12.

Encodings:

BibTeX
M. Yu. Loenko (2001)
Evaluating elementary functions with guaranteed precision,

Programming and Computer Software 27 (2), pp. 101–110.

External Links:

ISSN 0361-7688, Document, MathReview Entry, ZentralBlatt.

Referenced by:

§4.48(ii).

Encodings:

BibTeX
I. M. Longman (1956)
Note on a method for computing infinite integrals of oscillatory functions,

Proc. Cambridge Philos. Soc. 52 (4), pp. 764–768.

External Links:

Document, MathReview (D. J. Hofsommer), ZentralBlatt.

Referenced by:

§3.5(vii).

Encodings:

BibTeX
L. Lorch (1992)
On Bessel functions of equal order and argument,

Rend. Sem. Mat. Univ. Politec. Torino 50 (2), pp. 209–216 (1993).

External Links:

ISSN 0373-1243, MathReview (N. Hayek Calil), ZentralBlatt.

Referenced by:

§10.14.

Encodings:

BibTeX
L. Lorch, M. E. Muldoon and P. Szego (1970)
Higher monotonicity properties of certain Sturm-Liouville functions. III,

Canad. J. Math. 22, pp. 1238–1265.

External Links:

ISSN 0008-414X, MathReview (G. Sansone), ZentralBlatt.

Referenced by:

§10.21(ii).

Encodings:

BibTeX
L. Lorch, M. E. Muldoon and P. Szego (1972)
Higher monotonicity properties of certain Sturm-Liouville functions. IV,

Canad. J. Math. 24, pp. 349–368.

External Links:

ISSN 0008-414X, MathReview (G. Sansone), ZentralBlatt.

Referenced by:

§10.21(ii).

Encodings:

BibTeX
L. Lorch and M. E. Muldoon (2008)
Monotonic sequences related to zeros of Bessel functions,

Numer. Algorithms 49 (1-4), pp. 221–233.

External Links:

ISSN 1017-1398, Document, FullText, MathReview (Javier Segura), ZentralBlatt.

Referenced by:

§10.21(iv), §10.21(iv).

Encodings:

BibTeX
L. Lorch and P. Szego (1963)
Higher monotonicity properties of certain Sturm-Liouville functions.,

Acta Math. 109, pp. 55–73.

External Links:

ISSN 0001-5962, Document, MathReview (G. Sansone), ZentralBlatt.

Referenced by:

§10.21(ii).

Encodings:

BibTeX
L. Lorch and P. Szego (1964)
Monotonicity of the differences of zeros of Bessel functions as a function of order,

Proc. Amer. Math. Soc. 15 (1), pp. 91–96.

External Links:

ISSN 0002-9939, FullText, MathReview (F. W. J. Olver), ZentralBlatt.

Referenced by:

§10.21(ii).

Encodings:

BibTeX
L. Lorch and P. Szego (1990)
On the points of inflection of Bessel functions of positive order. I,

Canad. J. Math. 42 (5), pp. 933–948.

Notes:

Corrigenda see same journal, 42(6), p. 1132.

External Links:

ISSN 0008-414X, MathReview (A. McD. Mercer), ZentralBlatt.

Referenced by:

§10.21(iv).

Encodings:

BibTeX
L. Lorch and P. Szego (1995)
Monotonicity of the zeros of the third derivative of Bessel functions,

Methods Appl. Anal. 2 (1), pp. 103–111.

External Links:

ISSN 1073-2772, FullText, MathReview (N. Hayek Calil), ZentralBlatt.

Referenced by:

§10.21(iv).

Encodings:

BibTeX
L. Lorch (1984)
Inequalities for ultraspherical polynomials and the gamma function,

J. Approx. Theory 40 (2), pp. 115–120.

External Links:

ISSN 0021-9045, Document, MathReview (B. R. Bhonsle), ZentralBlatt.

Referenced by:

§18.14(i).

Encodings:

BibTeX
L. Lorch (1990)
Monotonicity in terms of order of the zeros of the derivatives of Bessel functions,

Proc. Amer. Math. Soc. 108 (2), pp. 387–389.

External Links:

ISSN 0002-9939, FullText, MathReview (M. E. Muldoon), ZentralBlatt.

Referenced by:

§10.21(iv), §10.21(iv).

Encodings:

BibTeX
L. Lorch (1993)
Some inequalities for the first positive zeros of Bessel functions,

SIAM J. Math. Anal. 24 (3), pp. 814–823.

External Links:

ISSN 0036-1410, Document, MathReview (R. K. Saxena), ZentralBlatt.

Referenced by:

§10.21(iv).

Encodings:

BibTeX
L. Lorch (1995)
The zeros of the third derivative of Bessel functions of order less than one,

Methods Appl. Anal. 2 (2), pp. 147–159.

External Links:

ISSN 1073-2772, FullText, MathReview (Evangelos Ifantis), ZentralBlatt.

Referenced by:

§10.21(iv), §10.21(iv).

Encodings:

BibTeX
L. Lorch (2002)
Comparison of a pair of upper bounds for a ratio of gamma functions,

Math. Balkanica (N.S.) 16 (1-4), pp. 195–202.

External Links:

ISSN 0205-3217, MathReview, ZentralBlatt.

Referenced by:

§5.6(i).

Encodings:

BibTeX
Lord Kelvin (1891)
Popular Lectures and Addresses,

Vol. 3, pp. 481–488.

Referenced by:

§36.13.

Encodings:

BibTeX
Lord Kelvin (1905)
Deep water ship-waves,

Phil. Mag. 9, pp. 733–757.

External Links:

ZentralBlatt.

Referenced by:

§36.13.

Encodings:

BibTeX
Lord Rayleigh (1945)
The Theory of Sound,

2nd edition, Dover Publications, New York.

Notes:

Photographic reproduction of the 1929 reprint of the edition of 1894–1896, published by Macmillan, London.

External Links:

MathReview, ZentralBlatt.

Referenced by:

§10.73(i).

Encodings:

BibTeX
H. A. Lorentz, A. Einstein, H. Minkowski and H. Weyl (1923)
The Principle of Relativity: A Collection of Original Memoirs on the Special and General Theory of Relativity,

Methuen and Co., Ltd., London.

Notes:

Translated from Das Relativitätsprinzip by W. Perrett and G. B. Jeffery. Reprinted by Dover Publications Inc., New York, 1952.

External Links:

MathReview, ZentralBlatt.

Referenced by:

§1.6(ii).

Encodings:

BibTeX
L. Lorentzen and H. Waadeland (1992)
Continued Fractions with Applications,

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

External Links:

ISBN 0-444-89265-6, MathReview (Olav Njåstad), ZentralBlatt.

Referenced by:

§1.12(ii), §1.12(iv), §1.12(v), §15.7, §18.13, ¶ ‣ §3.10(ii), ¶ ‣ §3.10(iii), ¶ ‣ §3.11(iv), §4.25, §4.39, §4.9(i), §4.9(ii), §5.10, §6.9, §7.18(v), §7.9.

Encodings:

BibTeX
H. Lotsch and M. Gray (1964)
Algorithm 244: Fresnel integrals,

Comm. ACM 7 (11), pp. 660–661.

Notes:

Includes Algol program, maximum accuracy 12D.

External Links:

ISSN 0001-0782, Document.

Referenced by:

§7.25(iv).

Encodings:

BibTeX
J. D. Louck (1958)
New recursion relation for the Clebsch-Gordan coefficients,

Phys. Rev. (2) 110 (4), pp. 815–816.

External Links:

Document, MathReview, ZentralBlatt.

Referenced by:

§34.3(iii).

Encodings:

BibTeX
E. R. Love (1970)
Changing the order of integration,

J. Austral. Math. Soc. 11, pp. 421–432.

Notes:

An addendum appears in Vol. 14, pp. 383-384, of the same journal.

External Links:

Document, MathReview (G. W. Johnson), ZentralBlatt.

Referenced by:

§1.5(v).

Encodings:

BibTeX
E. R. Love (1972a)
Addendum to: “Changing the order of integration”,

J. Austral. Math. Soc. 14, pp. 383–384.

External Links:

Document, MathReview (G. W. Johnson), ZentralBlatt.

Referenced by:

§1.5(v).

Encodings:

BibTeX
E. R. Love (1972b)
Two index laws for fractional integrals and derivatives,

J. Austral. Math. Soc. 14, pp. 385–410.

External Links:

Document, MathReview (C. Fox), ZentralBlatt.

Referenced by:

§1.15(vi), §1.15(vii).

Encodings:

BibTeX
L. Lovász, L. Pyber, D. J. A. Welsh and G. M. Ziegler (1995)
Combinatorics in Pure Mathematics,

in Handbook of Combinatorics, Vol. 2,

(M. Grötschel and L. Lovász Eds.), pp. 2039–2082.

External Links:

MathReview, ZentralBlatt.

Referenced by:

§26.19.

Encodings:

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A. N. Lowan and W. Horenstein (1942)
On the function $H(m,a,x)=\mathop{\exp\/}\nolimits(-ix)F(m+1-ia,2m+2;2ix)$ ,

J. Math. Phys. Mass. Inst. Tech. 21, pp. 264–283.

External Links:

ISSN 0097-1421, MathReview (M. C. Gray), ZentralBlatt.

Referenced by:

§33.7.

Encodings:

BibTeX
T. A. Lowdon (1970)
Integral representation of the Hankel function in terms of parabolic cylinder functions,

Quart. J. Mech. Appl. Math. 23 (3), pp. 315–327.

External Links:

Document, MathReview (T. Erber), ZentralBlatt.

Referenced by:

¶ ‣ §12.12, §12.16.

Encodings:

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D. W. Lozier and F. W. J. Olver (1993)
Airy and Bessel Functions by Parallel Integration of ODEs,

(D. E. Keyes, M. R. Leuze, L. R. Petzold and D. A. Reed Eds.), Philadelphia, PA, pp. 530–538.

External Links:

ISBN 0-89871-315-3.

Referenced by:

§10.74(ii), §3.7(iii), §9.17(ii).

Encodings:

BibTeX
D. W. Lozier and F. W. J. Olver (1994)
Numerical Evaluation of Special Functions,

in Mathematics of Computation 1943–1993: A Half-Century of Computational Mathematics (Vancouver, BC, 1993),

Proc. Sympos. Appl. Math., Vol. 48, pp. 79–125.

Notes:

An updated version exists online.

External Links:

FullText, MathReview (John P. Coleman), ZentralBlatt.

Referenced by:

Ch.3.

Encodings:

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D. W. Lozier and J. M. Smith (1981)
Algorithm 567: Extended-range arithmetic and normalized Legendre polynomials [A1], [C1],

ACM Trans. Math. Software 7 (1), pp. 141–146.

Notes:

Double-precision Fortran, minumum accuracy 13S

External Links:

ISSN 0098-3500, Document, TOMS module 567 (in GAMS).

Referenced by:

§14.34(ii).

Encodings:

BibTeX
D. W. Lozier (1980)
Numerical Solution of Linear Difference Equations,

NBSIR

Technical Report 80-1976, National Bureau of Standards, Gaithersburg, MD 20899.

Notes:

(Available from National Technical Information Service, Springfield, VA 22161.)

Referenced by:

§16.25, §3.6(vii).

Encodings:

BibTeX
D. W. Lozier (1993)
An underflow-induced graphics failure solved by SLI arithmetic,

(M. J. Irwin and G. A. Jullien Eds.), Washington, D.C., pp. 10–17.

External Links:

FullText.

Referenced by:

§3.1(iv).

Encodings:

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S. K. Lucas and H. A. Stone (1995)
Evaluating infinite integrals involving Bessel functions of arbitrary order,

J. Comput. Appl. Math. 64 (3), pp. 217–231.

External Links:

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

Referenced by:

¶ ‣ §10.74(vii).

Encodings:

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S. K. Lucas (1995)
Evaluating infinite integrals involving products of Bessel functions of arbitrary order,

J. Comput. Appl. Math. 64 (3), pp. 269–282.

External Links:

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

Referenced by:

¶ ‣ §10.74(vii).

Encodings:

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É. Lucas (1891)
Théorie des nombres. Tome I: Le calcul des nombres entiers, le calcul des nombres rationnels, la divisibilité arithmétique,

Gauthier-Villars, Paris (French).

External Links:

MathReview (W. J. LeVeque), ZentralBlatt.

Referenced by:

¶ ‣ §24.1, ¶ ‣ §24.1.

Encodings:

BibTeX
D. Ludwig (1966)
Uniform asymptotic expansions at a caustic,

Comm. Pure Appl. Math. 19, pp. 215–250.

External Links:

Document, MathReview (Colin Clark), ZentralBlatt.

Referenced by:

§36.12(iii), §36.14(i).

Encodings:

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N. A. Lukaševič and A. I. Yablonskiĭ (1967)
On a set of solutions of the sixth Painlevé equation,

Differ. Uravn. 3 (3), pp. 520–523 (Russian).

Notes:

In Russian. English translation: Differential Equations 3(3), pp. 264–266

External Links:

MathReview (J. Rausen).

Referenced by:

§32.10(vi).

Encodings:

BibTeX
N. A. Lukaševič (1965)
Elementary solutions of certain Painlevé equations,

Differ. Uravn. 1 (3), pp. 731–735 (Russian).

Notes:

In Russian. English translation: Differential Equations 1(3), pp. 561–564

External Links:

MathReview (Z. Nehari), ZentralBlatt.

Referenced by:

§32.10(iii), §32.10(iv), §32.9(i).

Encodings:

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N. A. Lukaševič (1967a)
Theory of the fourth Painlevé equation,

Differ. Uravn. 3 (5), pp. 771–780 (Russian).

Notes:

In Russian. English translation: Differential Equations 3(5), pp. 395–399

External Links:

MathReview (Z. Nehari), ZentralBlatt.

Referenced by:

§32.10(iv), §32.7(iv), §32.8(iv).

Encodings:

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N. A. Lukaševič (1967b)
On the theory of Painlevé’s third equation,

Differ. Uravn. 3 (11), pp. 1913–1923 (Russian).

Notes:

In Russian. English translation: Differential Equations 3(11), pp. 994–999

External Links:

MathReview (Z. Nehari), ZentralBlatt.

Referenced by:

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

Encodings:

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N. A. Lukaševič (1968)
Solutions of the fifth Painlevé equation,

Differ. Uravn. 4 (8), pp. 1413–1420 (Russian).

Notes:

In Russian. English translation: Differential Equations 4(8), pp. 732–735

External Links:

MathReview (C. E. Langenhop), ZentralBlatt.

Referenced by:

§32.10(v), §32.8(v).

Encodings:

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N. A. Lukaševič (1971)
The second Painlevé equation,

Differ. Uravn. 7 (6), pp. 1124–1125 (Russian).

Notes:

In Russian. English translation: Differential Equations 7(6), pp. 853–854

External Links:

MathReview (Z. Rubinstein), ZentralBlatt.

Referenced by:

§32.7(ii).

Encodings:

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Y. L. Luke and J. Wimp (1963)
Jacobi polynomial expansions of a generalized hypergeometric function over a semi-infinite ray,

Math. Comp. 17 (84), pp. 395–404.

External Links:

FullText, MathReview (I. A. Stegun), ZentralBlatt.

Referenced by:

§6.20(ii).

Encodings:

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Y. L. Luke (1959)
Expansion of the confluent hypergeometric function in series of Bessel functions,

Math. Tables Aids Comput. 13 (68), pp. 261–271.

External Links:

FullText, MathReview (A. Erdélyi), ZentralBlatt.

Referenced by:

§13.24(ii).

Encodings:

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Y. L. Luke (1962)
Integrals of Bessel Functions,

McGraw-Hill Book Co., Inc., New York.

External Links:

MathReview (A. E. Danese), ZentralBlatt.

Referenced by:

§10.22(ii), §10.22(iv), §10.22(vi), ¶ ‣ §10.43(iii), §10.43(vi), §11.7(v).

Encodings:

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Y. L. Luke (1968)
Approximations for elliptic integrals,

Math. Comp. 22 (103), pp. 627–634.

External Links:

FullText, MathReview, ZentralBlatt.

Referenced by:

§19.38.

Encodings:

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Y. L. Luke (1969a)
The Special Functions and their Approximations, Vol. 1,

Academic Press, New York.

External Links:

MathReview (R. G. Langebartel), ZentralBlatt.

Referenced by:

Ch.13, §15.10(ii), §15.12(ii), §15.12(iii), Ch.15, §16.11(iii), §16.11(iii), §16.17, §16.18, §16.18, §16.19, §16.20, §16.21, §16.22, §16.5, §16.5, §16.5, §16.7, §16.8(ii), §16.8(iii), Ch.16, Ch.3.

Encodings:

BibTeX
Y. L. Luke (1969b)
The Special Functions and their Approximations. Vol. 2,

Academic Press, New York.

External Links:

MathReview (R. G. Langebartel), ZentralBlatt.

Referenced by:

§10.23(iv), §10.60(iii), §11.10(viii), §11.4(iv), §11.9(ii), Ch.11, §12.20, §13.31(i), Ch.13, §16.10, §25.20, ¶ ‣ §3.11(iv), Ch.3, §4.47(iv), §5.23(ii), §5.7(i), §6.10(ii), §6.20(ii), §6.20(ii), §6.20(ii), §6.20(iii), §6.20(iii), §6.8, §7.24(ii), §7.24(iii), §7.6(ii), §7.8, ¶ ‣ §8.10, §8.10, ¶ ‣ §8.21(vi), §8.27(i), §8.27(i), Ch.8.

Encodings:

BibTeX
Y. L. Luke (1970)
Further approximations for elliptic integrals,

Math. Comp. 24 (109), pp. 191–198.

External Links:

FullText, MathReview, ZentralBlatt.

Referenced by:

§19.38.

Encodings:

BibTeX
Y. L. Luke (1971a)
Miniaturized tables of Bessel functions. II,

Math. Comp. 25 (116), pp. 789–795 and D14–E13.

Notes:

For Corrigendum see same journal 26(120), pp. A1–A7

External Links:

ISSN 0025-5718, FullText, MathReview, ZentralBlatt.

Referenced by:

¶ ‣ §10.76(ii).

Encodings:

BibTeX
Y. L. Luke (1971b)
Miniaturized tables of Bessel functions,

Math. Comp. 25 (114), pp. 323–330.

External Links:

ISSN 0025-5718, FullText, MathReview, ZentralBlatt.

Referenced by:

¶ ‣ §10.76(ii).

Encodings:

BibTeX
Y. L. Luke (1972)
Miniaturized tables of Bessel functions. III,

Math. Comp. 26 (117), pp. 237–240 and A14–B5.

External Links:

ISSN 0025-5718, FullText, MathReview, ZentralBlatt.

Referenced by:

¶ ‣ §10.76(ii).

Encodings:

BibTeX
Y. L. Luke (1975)
Mathematical Functions and their Approximations,

Academic Press Inc., New York.

External Links:

ISBN 0-12-459950-8, MathReview (N. M. Temme), ZentralBlatt.

Referenced by:

§10.75(i), ¶ ‣ §10.76(ii), ¶ ‣ §10.76(ii), ¶ ‣ §10.76(ii), ¶ ‣ §10.76(iii), §10.76(i), §11.15(i), Ch.11, §16.10, §16.2(iii), §16.2(iv), §16.20, §16.20, §16.22, §16.26, §16.3(i), §16.3(ii), Ch.16, §4.47(i), §4.47(iii), §4.47(iv), §5.22(i), §5.23(i), §5.23(ii), §5.23(iii), §8.1, §8.21(vi), §8.25(i), §8.27(i), §8.27(ii), §8.27(ii).

Encodings:

BibTeX
Y. L. Luke (1977a)
Algorithms for rational approximations for a confluent hypergeometric function,

Utilitas Math. 11, pp. 123–151.

External Links:

MathReview (F. Gotze), ZentralBlatt.

Referenced by:

§13.31(iii).

Encodings:

BibTeX
Y. L. Luke (1977b)
Algorithms for the Computation of Mathematical Functions,

Academic Press, New York.

External Links:

MathReview (Gh. Adam).

Referenced by:

§16.26.

Encodings:

BibTeX
J. Lund (1985)
Bessel transforms and rational extrapolation,

Numer. Math. 47 (1), pp. 1–14.

External Links:

ISSN 0029-599X, Document, MathReview (Vítĕzslav Veselý), ZentralBlatt.

Referenced by:

¶ ‣ §10.74(vii).

Encodings:

BibTeX
J. H. Luscombe and M. Luban (1998)
Simplified recursive algorithm for Wigner $3j$ and $6j$ symbols,

Phys. Rev. E 57 (6), pp. 7274–7277.

External Links:

Document.

Referenced by:

§34.13, §34.3(iii).

Encodings:

BibTeX
W. Luther (1995)
Highly accurate tables for elementary functions,

BIT 35 (3), pp. 352–360.

External Links:

ISSN 0006-3835, Document, MathReview, ZentralBlatt.

Referenced by:

¶ ‣ §4.45(i), §4.46.

Encodings:

BibTeX
R. J. Lyman and W. W. Edmonson (2001)
Linear prediction of bandlimited processes with flat spectral densities,

IEEE Trans. Signal Process. 49 (7), pp. 1564–1569.

External Links:

ISSN 1053-587X, Document, MathReview.

Referenced by:

§30.15(v).

Encodings:

BibTeX
A. E. Lynas-Gray (1993)
VOIGTL – A fast subroutine for Voigt function evaluation on vector processors,

Comput. Phys. Comm. 75 (1-2), pp. 135–142.

Notes:

Single-precision Fortran, minimum accuracy 13D.

External Links:

Document, Code, ZentralBlatt.

Referenced by:

§7.25(vi).

Encodings:

BibTeX
J. N. Lyness (1971)
Adjusted forms of the Fourier coefficient asymptotic expansion and applications in numerical quadrature,

Math. Comp. 25 (113), pp. 87–104.

External Links:

FullText, MathReview (J. Bryant), ZentralBlatt.

Referenced by:

§2.3(iv).

Encodings:

BibTeX
J. N. Lyness (1985)
Integrating some infinite oscillating tails,

J. Comput. Appl. Math. 12/13, pp. 109–117.

External Links:

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

Referenced by:

§3.5(vii).

Encodings:

BibTeX
J. L. López (2001)
Uniform asymptotic expansions of symmetric elliptic integrals,

Constr. Approx. 17 (4), pp. 535–559.

External Links:

ISSN 0176-4276, Document, MathReview (Valdir A. Menegatto), ZentralBlatt.

Referenced by:

§19.27(vi).

Encodings:

BibTeX
J. L. López and P. J. Pagola (2010)
The confluent hypergeometric functions $M(a,b;z)$ and $U(a,b;z)$ for large $b$ and $z$ ,

J. Comput. Appl. Math. 233 (6), pp. 1570–1576.

External Links:

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

Referenced by:

§13.8(ii), §13.8(ii).

Encodings:

BibTeX
J. L. López and N. M. Temme (1999a)
Approximation of orthogonal polynomials in terms of Hermite polynomials,

Methods Appl. Anal. 6 (2), pp. 131–146.

External Links:

ISSN 1073-2772, Pdf, MathReview, ZentralBlatt.

Referenced by:

§18.15(vi), §18.16(vi).

Encodings:

BibTeX
J. L. López and N. M. Temme (1999b)
Hermite polynomials in asymptotic representations of generalized Bernoulli, Euler, Bessel, and Buchholz polynomials,

J. Math. Anal. Appl. 239 (2), pp. 457–477.

External Links:

ISSN 0022-247X, Document, MathReview (A. G. Law), ZentralBlatt.

Referenced by:

§18.34(iii), §24.11.

Encodings:

BibTeX
J. L. López (1999)
Asymptotic expansions of the Whittaker functions for large order parameter,

Methods Appl. Anal. 6 (2), pp. 249–256.

Notes:

Dedicated to Richard A. Askey on the occasion of his 65th birthday, Part II

External Links:

ISSN 1073-2772, Pdf, MathReview, ZentralBlatt.

Referenced by:

§13.21(i), §13.24(ii).

Encodings:

BibTeX
J. L. López (2000)
Asymptotic expansions of symmetric standard elliptic integrals,

SIAM J. Math. Anal. 31 (4), pp. 754–775.

External Links:

ISSN 1095-7154, Document, MathReview (P. Anandani), ZentralBlatt.

Referenced by:

§19.27(vi), §2.6(ii).

Encodings:

BibTeX
J. L. López and N. M. Temme (2010)
Asymptotics and numerics of polynomials used in Tricomi and Buchholz expansions of Kummer functions,

Numer. Math. 116 (2), pp. 269–289.

External Links:

ISSN 0029-599X, Document, FullText, MathReview (Richard B. Paris), ZentralBlatt.

Referenced by:

§13.11, §13.11.

Encodings:

BibTeX