Bibliography W

♦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♦

E. L. Wachspress (2000)
Evaluating elliptic functions and their inverses,

Comput. Math. Appl. 39 (3-4), pp. 131–136.

External Links:

ISSN 0898-1221, Document, MathReview, ZentralBlatt.

Referenced by:

§22.20(ii), §22.20(v).

Encodings:

BibTeX
E. Wagner (1986)
Asymptotische Darstellungen der hypergeometrischen Funktion für große Parameter unterschiedlicher Größenordnung,

Z. Anal. Anwendungen 5 (3), pp. 265–276 (German).

External Links:

ISSN 0232-2064, MathReview (R. P. Soni), ZentralBlatt.

Referenced by:

§15.12(iii).

Encodings:

BibTeX
E. Wagner (1990)
Asymptotische Entwicklungen der Gaußschen hypergeometrischen Funktion für unbeschränkte Parameter,

Z. Anal. Anwendungen 9 (4), pp. 351–360 (German).

External Links:

ISSN 0232-2064, MathReview (T. Erber), ZentralBlatt.

Referenced by:

§15.12(ii).

Encodings:

BibTeX
E. Wagner (1988)
Asymptotische Entwicklungen der hypergeometrischen Funktion ${F}(a,b,c,z)$ für $|c|\to\infty$ und konstante Werte $a,b$ und $z$ ,

Demonstratio Math. 21 (2), pp. 441–458 (German).

External Links:

ISSN 0420-1213, MathReview (P. Anandani), ZentralBlatt.

Referenced by:

§15.12(ii), §15.12(ii).

Encodings:

BibTeX
S. S. Wagstaff (1978)
The irregular primes to 125000,

Math. Comp. 32 (142), pp. 583–591.

External Links:

FullText, Document, MathReview (Wells Johnson), ZentralBlatt.

Referenced by:

§24.20.

Encodings:

BibTeX
S. S. Wagstaff (2002)
Prime Divisors of the Bernoulli and Euler Numbers,

in Number Theory for the Millennium, III (Urbana, IL, 2000),

pp. 357–374.

External Links:

FullText, MathReview (Arnold M. Adelberg), ZentralBlatt.

Referenced by:

§24.20.

Encodings:

BibTeX
J. Waldvogel (2006)
Fast construction of the Fejér and Clenshaw-Curtis quadrature rules,

BIT 46 (1), pp. 195–202.

External Links:

ISSN 0006-3835, Document, MathReview Entry, ZentralBlatt.

Referenced by:

§3.5(iv).

Encodings:

BibTeX
J. Walker (1983)
Caustics: Mathematical curves generated by light shined through rippled plastic,

Scientific American 249, pp. 146–153.

Referenced by:

§36.14(ii).

Encodings:

BibTeX
J. Walker (1988)
Shadows cast on the bottom of a pool are not like other shadows. Why?,

Scientific American 259, pp. 86–89.

Referenced by:

§36.14(ii).

Encodings:

BibTeX
J. Walker (1989)
A drop of water becomes a gateway into the world of catastrophe optics,

Scientific American 261, pp. 120–123.

Referenced by:

§36.14(ii).

Encodings:

BibTeX
P. L. Walker (2012)
Reduction formulae for products of theta functions,

J. Res. Nat. Inst. Standards and Technology [In press.].

Referenced by:

(20.7.34), §20.7(ix).

Encodings:

BibTeX
P. L. Walker (1991)
Infinitely differentiable generalized logarithmic and exponential functions,

Math. Comp. 57 (196), pp. 723–733.

External Links:

ISSN 0025-5718, FullText, Document, MathReview (F. W. J. Olver), ZentralBlatt.

Referenced by:

§4.12.

Encodings:

BibTeX
P. L. Walker (1996)
Elliptic Functions. A Constructive Approach,

John Wiley & Sons Ltd., Chichester-New York.

External Links:

ISBN 0-471-96531-6, MathReview (Glenn Stevens), ZentralBlatt.

Referenced by:

§20.11(i), §20.4(i), §20.5(i), §20.5(iii), §20.6, §20.7(iv), §20.9(i), §20.9(ii), §20.9(ii), Ch.20, §22.1, §22.11, §22.12, §22.13(i), §22.16(i), §22.2, §22.20(ii), Figure 22.3.2, Figure 22.3.2, §22.4(i), §22.4(ii), §22.6(i), §22.6(iv), §22.7(i), §22.7(ii), §22.8(i), Ch.22, ¶ ‣ §23.1, §23.10(ii), §23.15(i), §23.17(i), §23.18, §23.2(i), §23.21(ii), §23.3(i), §23.3(ii), §23.5(i), §23.5(ii), §23.5(iii), §23.5(iv), §23.5(v), §23.6(i), §23.8(ii), Ch.23, §4.21(iii), Peter L. Walker.

Encodings:

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P. L. Walker (2003)
The analyticity of Jacobian functions with respect to the parameter $k$ ,

Proc. Roy. Soc. London Ser A 459, pp. 2569–2574.

External Links:

ISSN 1364-5021, Document, MathReview, ZentralBlatt.

Referenced by:

§22.17(ii), §22.2.

Encodings:

BibTeX
P. L. Walker (2007)
The zeros of Euler’s psi function and its derivatives,

J. Math. Anal. Appl. 332 (1), pp. 607–616.

External Links:

ISSN 0022-247X, Document, MathReview, ZentralBlatt (Mehdi Hassani).

Referenced by:

§5.4(iii).

Encodings:

BibTeX
P. L. Walker (2009)
The distribution of the zeros of Jacobian elliptic functions with respect to the parameter $k$ ,

Comput. Methods Funct. Theory 9 (2), pp. 579–591.

External Links:

ISSN 1617-9447, MathReview (M. K. Jain), ZentralBlatt.

Referenced by:

§22.4(i).

Encodings:

BibTeX
H. S. Wall (1948)
Analytic Theory of Continued Fractions,

D. Van Nostrand Company, Inc., New York.

Notes:

Reprinted by Chelsea Publishing, New York, 1973 and AMS Chelsea Publishing, Providence, RI, 2000.

External Links:

ISBN 0-8218-2106-7, MathReview (R. C. Buck), ZentralBlatt.

Referenced by:

§3.10(iii), §4.25, §4.9(i), §4.9(ii), Ch.4, §5.10.

Encodings:

BibTeX
Z. Wang and R. Wong (2002)
Uniform asymptotic expansion of $\mathop{J_{{\nu}}\/}\nolimits(\nu a)$ via a difference equation,

Numer. Math. 91 (1), pp. 147–193.

External Links:

ISSN 0029-599X, Document, MathReview (J. P. Singhal), ZentralBlatt.

Referenced by:

§10.20(ii).

Encodings:

BibTeX
Z. Wang and R. Wong (2003)
Asymptotic expansions for second-order linear difference equations with a turning point,

Numer. Math. 94 (1), pp. 147–194.

External Links:

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

Referenced by:

§2.9(iii).

Encodings:

BibTeX
Z. Wang and R. Wong (2005)
Linear difference equations with transition points,

Math. Comp. 74 (250), pp. 629–653.

External Links:

ISSN 0025-5718, Document, MathReview (B. G. Pachpatte), ZentralBlatt.

Referenced by:

§2.9(iii).

Encodings:

BibTeX
Z. Wang and R. Wong (2006)
Uniform asymptotics of the Stieltjes-Wigert polynomials via the Riemann-Hilbert approach,

J. Math. Pures Appl. (9) 85 (5), pp. 698–718.

External Links:

ISSN 0021-7824, Document, MathReview (Rabah Khaldi), ZentralBlatt.

Referenced by:

§18.29.

Encodings:

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Z. X. Wang and D. R. Guo (1989)
Special Functions,

World Scientific Publishing Co. Inc., Singapore.

Notes:

Translated from the Chinese by Guo and X. J. Xia

External Links:

ISBN 9971-50-659-9, MathReview (H. Hochstadt), ZentralBlatt.

Referenced by:

Ch.13, Ch.15.

Encodings:

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R. S. Ward (1987)
The Nahm equations, finite-gap potentials and Lamé functions,

J. Phys. A 20 (10), pp. 2679–2683.

External Links:

ISSN 0305-4470, Document, MathReview (James M. D’Archangelo), ZentralBlatt.

Referenced by:

§29.19(ii).

Encodings:

BibTeX
S. O. Warnaar (1998)
A note on the trinomial analogue of Bailey’s lemma,

J. Combin. Theory Ser. A 81 (1), pp. 114–118.

External Links:

ISSN 0097-3165, Document, MathReview (Anne Schilling), ZentralBlatt.

Referenced by:

¶ ‣ §17.12.

Encodings:

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L. C. Washington (1997)
Introduction to Cyclotomic Fields,

2nd edition, Springer-Verlag, New York.

External Links:

ISBN 0-387-94762-0, MathReview (T. Metsänkylä), ZentralBlatt.

Referenced by:

§24.10(i), §24.10(ii), §24.16(ii), §24.17(iii).

Encodings:

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W. Wasow (1965)
Asymptotic Expansions for Ordinary Differential Equations,

Interscience Publishers John Wiley & Sons, Inc., New York-London-Sydney.

Notes:

Reprinted by Krieger, New York, 1976 and Dover, New York, 1987.

External Links:

MathReview (N. D. Kazarinoff), ZentralBlatt.

Referenced by:

Ch.2, Ch.9.

Encodings:

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W. Wasow (1985)
Linear Turning Point Theory,

Applied Mathematical Sciences No. 54, Springer-Verlag, New York.

External Links:

ISBN 0-387-96046-5, MathReview (Anthony Leung), ZentralBlatt.

Referenced by:

Ch.9.

Encodings:

BibTeX
H. Watanabe (1995)
Solutions of the fifth Painlevé equation. I,

Hokkaido Math. J. 24 (2), pp. 231–267.

External Links:

ISSN 0385-4035, FullText, MathReview (Andrei A. Kapaev), ZentralBlatt.

Referenced by:

§32.10(v).

Encodings:

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T. Watanabe, M. Natori and T. Oguni (Eds.) (1994)
Mathematical Software for the P.C. and Work Stations – A Collection of Fortran 77 Programs,

North-Holland Publishing Co., Amsterdam.

Notes:

Translated from the 1989 Japanese original. With 1 IBM-PC floppy disk (5.25 inch) containing a large general purpose mathematical software collection written in Fortran, including some special function codes. Double precision.

External Links:

ISBN 0-444-82000-0, MathReview, ZentralBlatt.

Referenced by:

§ ‣ § Software Cross Index.

Encodings:

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B. M. Watrasiewicz (1967)
Some useful integrals of $\mathop{\mathrm{Si}\/}\nolimits(x),$ $\mathop{\mathrm{Ci}\/}\nolimits(x)$ and related integrals,

Optica Acta 14 (3), pp. 317–322.

External Links:

Document, MathReview (S. D. Bajpai).

Referenced by:

§6.14(iii), §6.7(iv).

Encodings:

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G. N. Watson (1910)
The cubic transformation of the hypergeometric function,

Quart. J. Pure and Applied Math. 41, pp. 70–79.

External Links:

ZentralBlatt.

Referenced by:

¶ ‣ §15.8(v), §15.8(v).

Encodings:

BibTeX
G. N. Watson (1935a)
Generating functions of class-numbers,

Compositio Math. 1, pp. 39–68.

External Links:

ISSN 0010-437X, FullText, MathReview Entry, ZentralBlatt.

Referenced by:

§20.7(v), §20.8.

Encodings:

BibTeX
G. N. Watson (1935b)
The surface of an ellipsoid,

Quart. J. Math., Oxford Ser. 6, pp. 280–287.

External Links:

Document, ZentralBlatt.

Referenced by:

§19.33(i).

Encodings:

BibTeX
G. N. Watson (1937)
Two tables of partitions,

Proc. London Math. Soc. (2) 42, pp. 550–556.

External Links:

Document, ZentralBlatt.

Referenced by:

§27.21.

Encodings:

BibTeX
G. N. Watson (1944)
A Treatise on the Theory of Bessel Functions,

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

Notes:

Reprinted in 1995.

External Links:

MathReview (G. Szegö), ZentralBlatt.

Referenced by:

§1.13(v), §10.1, §10.10, §10.12, §10.13, §10.14, §10.14, §10.15, ¶ ‣ §10.16, §10.17(iii), §10.18(iii), §10.19(ii), §10.19(iii), §10.2(ii), §10.21(i), §10.21(i), §10.21(xiii), §10.21(ii), §10.21(iii), §10.21(iv), §10.21(vi), §10.22(i), §10.22(ii), §10.22(iv), §10.22(vi), ¶ ‣ §10.23(iii), ¶ ‣ §10.23(iii), ¶ ‣ §10.23(iii), §10.23(i), §10.23(ii), §10.23(iii), §10.27, §10.29(i), §10.29(ii), §10.31, §10.32(i), §10.32(ii), §10.32(iii), §10.32(iv), §10.34, §10.4, §10.40(i), §10.40(ii), §10.42, §10.42, §10.43(iv), §10.43(vi), ¶ ‣ §10.44(ii), §10.54, §10.6(i), §10.6(ii), §10.60(iii), §10.60(iv), §10.8, §10.9(i), §10.9(ii), §10.9(iii), §10.9(iv), Ch.10, §11.10(i), §11.10(ii), §11.10(iii), §11.10(v), §11.10(vi), §11.10(ix), §11.11(i), §11.11(iii), §11.11(iii), §11.2(i), §11.2(ii), §11.4(ii), §11.4(v), §11.5(i), §11.5(iii), §11.6(i), §11.6(iii), §11.6(iii), §11.6(iii), §11.7(ii), ¶ ‣ §11.9(i), §11.9(iii), §11.9(iv), Ch.11, §18.17(v), ¶ ‣ §2.5(i).

Encodings:

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G. N. Watson (1949)
A table of Ramanujan’s function $\mathop{\tau\/}\nolimits(n)$ ,

Proc. London Math. Soc. (2) 51, pp. 1–13.

External Links:

Document, MathReview (D. H. Lehmer), ZentralBlatt.

Referenced by:

§27.21.

Encodings:

BibTeX
J. K. G. Watson (1999)
Asymptotic approximations for certain 6- $j$ and 9- $j$ symbols,

J. Phys. A 32 (39), pp. 6901–6902.

External Links:

ISSN 0305-4470, Document, MathReview, ZentralBlatt.

Referenced by:

§34.8, §34.8.

Encodings:

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J. V. Wehausen and E. V. Laitone (1960)
Surface Waves,

in Handbuch der Physik, Vol. 9, Part 3,

pp. 446–778.

External Links:

Online edition, MathReview (F. Ursell).

Referenced by:

§11.12.

Encodings:

BibTeX
G. Wei and B. E. Eichinger (1993)
Asymptotic expansions of some matrix argument hypergeometric functions, with applications to macromolecules,

Ann. Inst. Statist. Math. 45 (3), pp. 467–475.

External Links:

ISSN 0020-3157, Document, MathReview (N. K. Thakare), ZentralBlatt.

Referenced by:

§35.9.

Encodings:

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T. Weider (1999)
Algorithm 794: Numerical Hankel transform by the Fortran program HANKEL,

ACM Trans. Math. Software 25 (2), pp. 240–250.

Notes:

Double-precision Fortran, maximum accuracy 10S.

External Links:

ISSN 0098-3500, Document, TOMS module 794 (in GAMS).

Referenced by:

§10.77(iii), §10.77(ix).

Encodings:

BibTeX
A. Weil (1999)
Elliptic Functions According to Eisenstein and Kronecker,

Classics in Mathematics, Springer-Verlag, Berlin.

Notes:

Reprint of the 1976 original

External Links:

ISBN 3-540-65036-9, MathReview, ZentralBlatt.

Referenced by:

§22.12, §23.8(ii).

Encodings:

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M. I. Weinstein and J. B. Keller (1985)
Hill’s equation with a large potential,

SIAM J. Appl. Math. 45 (2), pp. 200–214.

External Links:

ISSN 0036-1399, Document, MathReview (H. Hochstadt), ZentralBlatt.

Referenced by:

§29.7(ii).

Encodings:

BibTeX
M. I. Weinstein and J. B. Keller (1987)
Asymptotic behavior of stability regions for Hill’s equation,

SIAM J. Appl. Math. 47 (5), pp. 941–958.

External Links:

ISSN 0036-1399, Document, MathReview (Ekkehard Wagenführer), ZentralBlatt.

Referenced by:

§28.29(iii).

Encodings:

BibTeX
G. Weiss (1965)
Harmonic Analysis,

in Studies in Real and Complex Analysis,

Studies in Mathematics, Vol. 3, pp. 124–178.

External Links:

MathReview, ZentralBlatt.

Referenced by:

§1.15(iii), §1.15(iv), §1.15(v).

Encodings:

BibTeX
E. J. Weniger (1989)
Nonlinear sequence transformations for the acceleration of convergence and the summation of divergent series,

Computer Physics Reports 10 (5-6), pp. 189–371.

External Links:

Document.

Referenced by:

§2.11(vi), §3.9(v), §3.9(vi).

Encodings:

BibTeX
E. J. Weniger (1996)
Computation of the Whittaker function of the second kind by summing its divergent asymptotic series with the help of nonlinear sequence transformations,

Computers in Physics 10 (5), pp. 496–503.

External Links:

Document.

Referenced by:

§2.11(vi), §2.11(vi).

Encodings:

BibTeX
E. J. Weniger and J. Čížek (1990)
Rational approximations for the modified Bessel function of the second kind,

Comput. Phys. Comm. 59 (3), pp. 471–493.

External Links:

ISSN 0010-4655, Document, MathReview, ZentralBlatt.

Referenced by:

¶ ‣ §10.76(ii).

Encodings:

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E. J. Weniger (2003)
A rational approximant for the digamma function,

Numer. Algorithms 33 (1-4), pp. 499–507.

Notes:

International Conference on Numerical Algorithms, Vol. I (Marrakesh, 2001)

External Links:

ISSN 1017-1398, Document, MathReview, ZentralBlatt.

Referenced by:

§3.9(vi), §5.23(i).

Encodings:

BibTeX
E. J. Weniger (2007)
Asymptotic Approximations to Truncation Errors of Series Representations for Special Functions,

in Algorithms for Approximation,

(J. Levesley Ed.), pp. 331–348.

External Links:

ISBN 3-540-33283-9, Document, MathReview Entry, ZentralBlatt.

Referenced by:

¶ ‣ §2.10(i).

Encodings:

BibTeX
H. Werner, J. Stoer and W. Bommas (1967)
Rational Chebyshev approximation,

Numer. Math. 10 (4), pp. 289–306.

External Links:

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

Referenced by:

§3.11(iii).

Encodings:

BibTeX
J. A. Wheeler (1937)
Wave functions for large arguments by the amplitude-phase method,

Phys. Rev. 52, pp. 1123–1127.

External Links:

Document, ZentralBlatt.

Referenced by:

§33.5(ii).

Encodings:

BibTeX
A. D. Wheelon (1968)
Tables of Summable Series and Integrals Involving Bessel Functions,

Holden-Day, San Francisco, CA.

External Links:

MathReview, ZentralBlatt.

Referenced by:

§10.22(vi), §10.23(iv), §10.43(vi).

Encodings:

BibTeX
F. J. W. Whipple (1927)
Some transformations of generalized hypergeometric series,

Proc. London Math. Soc. (2) 26 (2), pp. 257–272.

External Links:

Document, ZentralBlatt.

Referenced by:

§16.6.

Encodings:

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C. S. Whitehead (1911)
On a generalization of the functions $\mathrm{ber}$ x, $\mathrm{bei}$ x, $\mathrm{ker}$ x, $\mathrm{kei}$ x,

Quart. J. Pure Appl. Math. 42, pp. 316–342.

External Links:

ZentralBlatt.

Referenced by:

§10.61(iii), §10.61(iv), §10.65(i), §10.65(ii), §10.65(iii), §10.68(iii).

Encodings:

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G. B. Whitham (1974)
Linear and Nonlinear Waves,

John Wiley & Sons, New York.

Notes:

Reprinted in 1999.

External Links:

ISBN 0471359424, MathReview, ZentralBlatt.

Referenced by:

§9.16.

Encodings:

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E. T. Whittaker and G. N. Watson (1927)
A Course of Modern Analysis,

4th edition, Cambridge University Press.

Notes:

Reprinted in 1996. Table errata: Math. Comp. v. 36 (1981), no. 153, p. 319.

External Links:

MathReview, ZentralBlatt.

Referenced by:

§1.3(iii), §10.1, §12.11(i), §12.9(i), Ch.13, §15.6, Ch.15, Ch.19, ¶ ‣ §20.1, ¶ ‣ §20.1, §20.13, §20.2(i), §20.2(ii), §20.2(iii), §20.2(iv), §20.4(i), §20.4(ii), §20.5(ii), §20.7(ii), §20.7(iv), §20.7(viii), §20.9(i), §20.9(ii), §20.9(ii), Ch.20, §22.11, §22.13(i), §22.13(ii), §22.14(i), §22.14(iii), §22.14(iv), §22.15(i), §22.16(ii), §22.16(iii), ¶ ‣ §22.18(i), §22.18(iv), §22.2, §22.4(i), §22.4(ii), §22.4(iii), §22.5(i), §22.6(i), §22.6(iv), §22.7(i), §22.7(ii), §22.8(i), §22.8(ii), §22.8(iii), §22.8(iii), Ch.22, ¶ ‣ §23.1, §23.10(i), §23.2(ii), §23.2(iii), ¶ ‣ §23.22(ii), §23.3(i), §23.3(ii), §23.6(i), Ch.23, ¶ ‣ §24.1, Table 28.1.1, §29.12(iii), Ch.29, §31.8, §31.8, Ch.4, ¶ ‣ §5.11(i), §5.11(ii), §5.17, §5.8, ¶ ‣ §5.9(i), §5.9(i), §5.9(ii), Ch.5.

Encodings:

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E. T. Whittaker (1902)
On the functions associated with the parabolic cylinder in harmonic analysis,

Proc. London Math. Soc. 35, pp. 417–427.

External Links:

Document, ZentralBlatt.

Referenced by:

§12.1, §12.5(i), §12.5(ii), §12.9(i).

Encodings:

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E. T. Whittaker (1964)
A Treatise on the Analytical Dynamics of Particles and Rigid Bodies,

4th edition, Cambridge University Press, Cambridge.

Notes:

Reprinted in 1988.

External Links:

ISBN 0-521-35883-3, MathReview, ZentralBlatt.

Referenced by:

§22.19(i), §22.19(iv), §22.19(v), §23.21(i).

Encodings:

BibTeX
D. V. Widder (1979)
The Airy transform,

Amer. Math. Monthly 86 (4), pp. 271–277.

External Links:

ISSN 0002-9890, FullText, Document, MathReview (A. G. Ramm), ZentralBlatt.

Referenced by:

§9.10(v), §9.10(ix).

Encodings:

BibTeX
D. V. Widder (1941)
The Laplace Transform,

Princeton Mathematical Series, v. 6, Princeton University Press, Princeton, NJ.

External Links:

FullText, MathReview (J. D. Tamarkin), ZentralBlatt.

Referenced by:

§1.14(vi), §1.15(viii).

Encodings:

BibTeX

R. L. Wiegel (1960)
A presentation of cnoidal wave theory for practical application,

J. Fluid Mech. 7 (2), pp. 273–286.

External Links:

Document, MathReview (T. B. Benjamin), ZentralBlatt.

Referenced by:

§21.9.

Encodings:

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E. P. Wigner (1959)
Group Theory and its Application to the Quantum Mechanics of Atomic Spectra,

Pure and Applied Physics. Vol. 5, Academic Press, New York.

Notes:

Expanded and improved ed. Translated from the German by J. J. Griffin.

External Links:

ISBN 0-12-750550-4, MathReview (A. S. Wightman), ZentralBlatt.

Referenced by:

§34.12.

Encodings:

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H. S. Wilf and D. Zeilberger (1992a)
An algorithmic proof theory for hypergeometric (ordinary and “ $q$ ”) multisum/integral identities,

Invent. Math. 108, pp. 575–633.

External Links:

ISSN 0020-9910, Document, MathReview (David R. Masson), ZentralBlatt.

Referenced by:

§16.4(iii).

Encodings:

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H. S. Wilf and D. Zeilberger (1992b)
Rational function certification of multisum/integral/“ $q$ ” identities,

Bull. Amer. Math. Soc. (N.S.) 27 (1), pp. 148–153.

External Links:

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

Referenced by:

§16.4(iii).

Encodings:

BibTeX
H. S. Wilf (1994)
generatingfunctionology,

2nd edition, Academic Press Inc., Boston, MA.

Notes:

A 3rd edition was published in 2006 by A.K. Peters, Ltd., Wellesley, MA.

External Links:

ISBN 0-12-751956-4, MathReview, ZentralBlatt.

Referenced by:

¶ ‣ §26.18, §26.7(i).

Encodings:

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J. H. Wilkinson (1988)
The Algebraic Eigenvalue Problem,

Monographs on Numerical Analysis. Oxford Science Publications, The Clarendon Press, Oxford University Press, Oxford.

Notes:

Paperback reprint of original edition, published in 1965 by Clarendon Press, Oxford.

External Links:

ISBN 0-19-853418-3, MathReview, ZentralBlatt.

Referenced by:

§3.2(v), §3.2(vi), §3.2(vii).

Encodings:

BibTeX
C. A. Wills, J. M. Blair and P. L. Ragde (1982)
Rational Chebyshev approximations for the Bessel functions $J_{{0}}(x)$ , $J_{{1}}(x)$ , $Y_{{0}}(x)$ , $Y_{{1}}(x)$ ,

Math. Comp. 39 (160), pp. 617–623.

Notes:

Tables on microfiche

External Links:

ISSN 0025-5718, FullText, MathReview (C. W. Clenshaw), ZentralBlatt.

Referenced by:

¶ ‣ §10.75(iii).

Encodings:

BibTeX
J. A. Wilson (1978)
Hypergeometric Series, Recurrence Relations and Some New Orthogonal Polynomials,

Ph.D. Thesis, University of Wisconsin, Madison, WI.

Referenced by:

§16.4(iii), §16.4(iii), §16.4(iii).

Encodings:

BibTeX
J. A. Wilson (1980)
Some hypergeometric orthogonal polynomials,

SIAM J. Math. Anal. 11 (4), pp. 690–701.

External Links:

ISSN 0036-1410, Document, MathReview (R. G. Buschman), ZentralBlatt.

Referenced by:

§18.25(i), §18.25(ii), §18.25(iii), §18.26(i), §18.26(ii).

Encodings:

BibTeX
J. A. Wilson (1991)
Asymptotics for the ${}_{4}F_{3}$ polynomials,

J. Approx. Theory 66 (1), pp. 58–71.

External Links:

ISSN 0021-9045, Document, MathReview (R. G. Buschman), ZentralBlatt.

Referenced by:

§18.26(v).

Encodings:

BibTeX
J. Wimp (1964)
A class of integral transforms,

Proc. Edinburgh Math. Soc. (2) 14, pp. 33–40.

External Links:

Document, MathReview (B. R. Bhonsle), ZentralBlatt.

Referenced by:

§13.23(iv).

Encodings:

BibTeX
J. Wimp (1965)
On the zeros of a confluent hypergeometric function,

Proc. Amer. Math. Soc. 16 (2), pp. 281–283.

External Links:

FullText, Document, MathReview (L. J. Slater), ZentralBlatt.

Referenced by:

§13.9(ii).

Encodings:

BibTeX
J. Wimp (1968)
Recursion formulae for hypergeometric functions,

Math. Comp. 22 (102), pp. 363–373.

External Links:

FullText, Document, MathReview (S. D. Bajpai), ZentralBlatt.

Referenced by:

§16.3(ii).

Encodings:

BibTeX
J. Wimp (1981)
Sequence Transformations and their Applications,

Mathematics in Science and Engineering, Vol. 154, Academic Press Inc., New York.

External Links:

ISBN 0-12-757940-0, MathReview (Jan Zítko), ZentralBlatt.

Referenced by:

§3.9(vi).

Encodings:

BibTeX
J. Wimp (1984)
Computation with Recurrence Relations,

Pitman, Boston, MA.

External Links:

ISBN 0-273-08508-5, MathReview (S. Conde), ZentralBlatt.

Referenced by:

¶ ‣ §13.29(iv), §16.25, §2.9(iii), ¶ ‣ §3.10(iii), §3.6(iii), §3.6(v), §3.6(vii).

Encodings:

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J. Wimp (1985)
Some explicit Padé approximants for the function $\Phi^{{\prime}}/\Phi$ and a related quadrature formula involving Bessel functions,

SIAM J. Math. Anal. 16 (4), pp. 887–895.

External Links:

ISSN 0036-1410, Document, MathReview (Wyman Fair), ZentralBlatt.

Referenced by:

§13.31(ii).

Encodings:

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J. Wimp (1987)
Explicit formulas for the associated Jacobi polynomials and some applications,

Canad. J. Math. 39 (4), pp. 983–1000.

External Links:

ISSN 0008-414X, MathReview (W. A. Al-Salam), ZentralBlatt.

Referenced by:

¶ ‣ §18.30, §18.30.

Encodings:

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J. Wishart (1928)
The generalised product moment distribution in samples from a normal multivariate population,

Biometrika 20A, pp. 32–52.

External Links:

FullText, Document, ZentralBlatt.

Referenced by:

§35.3(i), §35.3(ii).

Encodings:

BibTeX
E. Witten (1987)
Elliptic genera and quantum field theory,

Comm. Math. Phys. 109 (4), pp. 525–536.

External Links:

ISSN 0010-3616, Document, MathReview (J. Stasheff), ZentralBlatt.

Referenced by:

§23.21(iv).

Encodings:

BibTeX
M. E. Wojcicki (1961)
Algorithm 44: Bessel functions computed recursively,

Comm. ACM 4 (4), pp. 177–178.

Notes:

Includes Algol code, maximum accuracy 8S.

External Links:

ISSN 0001-0782, Document.

Referenced by:

§10.77(ii).

Encodings:

BibTeX
G. Wolf (1998)
On the central connection problem for the double confluent Heun equation,

Math. Nachr. 195, pp. 267–276.

External Links:

ISSN 0025-584X, MathReview, ZentralBlatt.

Referenced by:

¶ ‣ §31.12.

Encodings:

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G. Wolf (2008)
On the asymptotic behavior of the Fourier coefficients of Mathieu functions,

J. Res. Nat. Inst. Standards Tech. 113 (1), pp. 11–15.

External Links:

ISSN 1044-677X, FullText.

Referenced by:

§28.4(vii).

Encodings:

BibTeX
Wolfram’s Mathworld (Web Site)

Notes:

A free resource from Wolfram Research built with Mathematica technology.

External Links:

Home Page.

Referenced by:

§27.22, § ‣ § Software Cross Index.

Encodings:

BibTeX
R. Wong and T. Lang (1990)
Asymptotic behaviour of the inflection points of Bessel functions,

Proc. Roy. Soc. London Ser. A 431, pp. 509–518.

External Links:

ISSN 0962-8444, FullText, Document, MathReview (A. McD. Mercer), ZentralBlatt.

Referenced by:

§10.21(vi), §10.21(vi).

Encodings:

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R. Wong and T. Lang (1991)
On the points of inflection of Bessel functions of positive order. II,

Canad. J. Math. 43 (3), pp. 628–651.

External Links:

ISSN 0008-414X, MathReview (Evangelos Ifantis), ZentralBlatt.

Referenced by:

§10.21(iv).

Encodings:

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R. Wong and H. Li (1992a)
Asymptotic expansions for second-order linear difference equations. II,

Stud. Appl. Math. 87 (4), pp. 289–324.

External Links:

ISSN 0022-2526, MathReview (Shao Zhu Chen), ZentralBlatt.

Referenced by:

§2.9(ii).

Encodings:

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R. Wong and H. Li (1992b)
Asymptotic expansions for second-order linear difference equations,

J. Comput. Appl. Math. 41 (1-2), pp. 65–94.

External Links:

ISSN 0377-0427, Document, MathReview (Shao Zhu Chen), ZentralBlatt.

Referenced by:

§2.9(i), §2.9(ii).

Encodings:

BibTeX
R. Wong and J. F. Lin (1978)
Asymptotic expansions of Fourier transforms of functions with logarithmic singularities,

J. Math. Anal. Appl. 64 (1), pp. 173–180.

External Links:

Document, MathReview (B. L. Gupta), ZentralBlatt.

Referenced by:

§2.3(iv).

Encodings:

BibTeX
R. Wong and M. Wyman (1974)
The method of Darboux,

J. Approximation Theory 10 (2), pp. 159–171.

External Links:

Document, MathReview (M. E. Noble), ZentralBlatt.

Referenced by:

¶ ‣ §2.10(iv).

Encodings:

BibTeX
R. Wong and H. Y. Zhang (2007)
Asymptotic solutions of a fourth order differential equation,

Stud. Appl. Math. 118 (2), pp. 133–152.

External Links:

ISSN 0022-2526, Document, MathReview Entry.

Referenced by:

§2.8(vi).

Encodings:

BibTeX
R. Wong and H. Y. Zhang (2009a)
On the connection formulas of the fourth Painlevé transcendent,

Anal. Appl. (Singap.) 7 (4), pp. 419–448.

External Links:

ISSN 0219-5305, Document, MathReview Entry, ZentralBlatt.

Referenced by:

§32.13(ii).

Encodings:

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R. Wong and H. Y. Zhang (2009b)
On the connection formulas of the third Painlevé transcendent,

Discrete Contin. Dyn. Syst. 23 (1-2), pp. 541–560.

External Links:

ISSN 1078-0947, Document, MathReview (Galina V. Filipuk), ZentralBlatt.

Referenced by:

§32.13(ii).

Encodings:

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R. Wong and J.-M. Zhang (1994a)
Asymptotic monotonicity of the relative extrema of Jacobi polynomials,

Canad. J. Math. 46 (6), pp. 1318–1337.

External Links:

ISSN 0008-414X, MathReview (S. I. Drobnies), ZentralBlatt.

Referenced by:

¶ ‣ §18.14(iii).

Encodings:

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R. Wong and J.-M. Zhang (1994b)
On the relative extrema of the Jacobi polynomials $P_{n}^{{(0,-1)}}(x)$ ,

SIAM J. Math. Anal. 25 (2), pp. 776–811.

External Links:

ISSN 0036-1410, Document, MathReview (G. Gasper), ZentralBlatt.

Referenced by:

¶ ‣ §18.14(iii).

Encodings:

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R. Wong and J.-M. Zhang (1997)
Asymptotic expansions of the generalized Bessel polynomials,

J. Comput. Appl. Math. 85 (1), pp. 87–112.

External Links:

ISSN 0377-0427, Document, MathReview, ZentralBlatt.

Referenced by:

§18.34(iii).

Encodings:

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R. Wong and Y.-Q. Zhao (1999a)
Smoothing of Stokes’s discontinuity for the generalized Bessel function. II,

Proc. Roy. Soc. London Ser. A 455, pp. 3065–3084.

External Links:

ISSN 1364-5021, Document, MathReview, ZentralBlatt.

Referenced by:

§10.46.

Encodings:

BibTeX
R. Wong and Y.-Q. Zhao (1999b)
Smoothing of Stokes’s discontinuity for the generalized Bessel function,

Proc. Roy. Soc. London Ser. A 455, pp. 1381–1400.

External Links:

ISSN 1364-5021, Document, MathReview, ZentralBlatt.

Referenced by:

§10.46.

Encodings:

BibTeX
R. Wong and Y.-Q. Zhao (2003)
Estimates for the error term in a uniform asymptotic expansion of the Jacobi polynomials,

Anal. Appl. (Singap.) 1 (2), pp. 213–241.

External Links:

ISSN 0219-5305, Document, MathReview (Eberhard Wagner), ZentralBlatt.

Referenced by:

§18.15(i).

Encodings:

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R. Wong and Y. Zhao (2002a)
Exponential asymptotics of the Mittag-Leffler function,

Constr. Approx. 18 (3), pp. 355–385.

External Links:

ISSN 0176-4276, Document, MathReview, ZentralBlatt.

Referenced by:

§10.46.

Encodings:

BibTeX
R. Wong and Y. Zhao (2002b)
Gevrey asymptotics and Stieltjes transforms of algebraically decaying functions,

Proc. Roy. Soc. London Ser. A 458, pp. 625–644.

External Links:

ISSN 1364-5021, Document, MathReview, ZentralBlatt.

Referenced by:

§2.11(v).

Encodings:

BibTeX
R. Wong and Y. Zhao (2004)
Uniform asymptotic expansion of the Jacobi polynomials in a complex domain,

Proc. Roy. Soc. London Ser. A 460, pp. 2569–2586.

External Links:

ISSN 1364-5021, Document, MathReview (Pet”r Rusev), ZentralBlatt.

Referenced by:

§18.15(i).

Encodings:

BibTeX
R. Wong and Y. Zhao (2005)
On a uniform treatment of Darboux’s method,

Constr. Approx. 21 (2), pp. 225–255.

External Links:

ISSN 0176-4276, Document, MathReview Entry, ZentralBlatt.

Referenced by:

¶ ‣ §2.10(iv).

Encodings:

BibTeX
R. Wong (1973a)
An asymptotic expansion of ${W}_{{k,\, m}}(z)$ with large variable and parameters,

Math. Comp. 27 (122), pp. 429–436.

External Links:

FullText, Document, MathReview (J. A. Donaldson), ZentralBlatt.

Referenced by:

§13.19.

Encodings:

BibTeX
R. Wong (1973b)
On uniform asymptotic expansion of definite integrals,

J. Approximation Theory 7 (1), pp. 76–86.

External Links:

Document, MathReview (L. Berg), ZentralBlatt.

Referenced by:

§8.11(v).

Encodings:

BibTeX
R. Wong (1976)
Error bounds for asymptotic expansions of Hankel transforms,

SIAM J. Math. Anal. 7 (6), pp. 799–808.

External Links:

ISSN 1095-7154, Document, MathReview (John S. Lew), ZentralBlatt.

Referenced by:

§10.22(v).

Encodings:

BibTeX
R. Wong (1977)
Asymptotic expansions of Hankel transforms of functions with logarithmic singularities,

Comput. Math. Appl. 3 (4), pp. 271–286.

External Links:

ISSN 0886-9561, Document, MathReview, ZentralBlatt.

Referenced by:

§10.22(v).

Encodings:

BibTeX
R. Wong (1979)
Explicit error terms for asymptotic expansions of Mellin convolutions,

J. Math. Anal. Appl. 72 (2), pp. 740–756.

External Links:

ISSN 0022-247X, Document, MathReview (John S. Lew), ZentralBlatt.

Referenced by:

§2.6(ii), §2.6(iv).

Encodings:

BibTeX
R. Wong (1981)
Asymptotic expansions of the Kontorovich-Lebedev transform,

Appl. Anal. 12 (3), pp. 161–172.

External Links:

ISSN 0003-6811, Document, MathReview (E. R. Love), ZentralBlatt.

Referenced by:

§10.43(v).

Encodings:

BibTeX
R. Wong (1982)
Quadrature formulas for oscillatory integral transforms,

Numer. Math. 39 (3), pp. 351–360.

External Links:

ISSN 0029-599X, Document, MathReview (A.J. Rodrigues), ZentralBlatt.

Referenced by:

¶ ‣ §10.74(vii), §3.5(vii).

Encodings:

BibTeX
R. Wong (1983)
Applications of some recent results in asymptotic expansions,

Congr. Numer. 37, pp. 145–182.

External Links:

ISSN 0384-9864, MathReview (F. W. J. Olver), ZentralBlatt.

Referenced by:

§19.27(vi).

Encodings:

BibTeX
R. Wong (1989)
Asymptotic Approximations of Integrals,

Academic Press Inc., Boston-New York.

Notes:

Reprinted with corrections by SIAM, Philadelphia, PA, 2001.

External Links:

ISBN 0-12-762535-6, MathReview (F. Ursell), ZentralBlatt.

Referenced by:

§1.14(iv), §1.14(vii), §1.15(iv), §1.16(i), §1.16(ii), §1.16(iii), §1.16(iv), §1.16(v), §1.16(vi), §1.16(vii), §14.26, Ch.14, ¶ ‣ §2.10(iv), §2.3(i), §2.3(ii), §2.3(iii), §2.3(v), §2.4(i), §2.4(ii), §2.4(iv), §2.4(v), §2.4(vi), ¶ ‣ §2.5(iii), §2.5(i), §2.5(ii), §2.5(ii), §2.5(ii), §2.5(iii), ¶ ‣ §2.6(iii), §2.6(i), §2.6(i), §2.6(ii), §2.6(ii), §2.6(iii), §2.6(iv), §2.6(iv), Ch.2, §7.20(i), Ch.8, Ch.9, Roderick S. C. Wong.

Encodings:

BibTeX
R. Wong (1995)
Error bounds for asymptotic approximations of special functions,

Ann. Numer. Math. 2 (1-4), pp. 181–197.

Notes:

Special functions (Torino, 1993)

External Links:

ISSN 1021-2655, MathReview (Andrei Martínez Finkelshtein), ZentralBlatt.

Referenced by:

§10.21(vi).

Encodings:

BibTeX
P. M. Woodward and A. M. Woodward (1946)
Four-figure tables of the Airy function in the complex plane,

Philos. Mag. (7) 37, pp. 236–261.

External Links:

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

Referenced by:

§9.18(iii).

Encodings:

BibTeX
World Combinatorics Exchange (Web Site)

Notes:

A service of the Electronic Journal of Combinatorics with links to databases, software, and other resources.

External Links:

World Combinatorics Exchange.

Referenced by:

§26.22.

Encodings:

BibTeX
J. W. Wrench (1968)
Concerning two series for the gamma function,

Math. Comp. 22 (103), pp. 617–626.

External Links:

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

Referenced by:

§5.11(i), §5.7(i), §5.7(i).

Encodings:

BibTeX
E. M. Wright (1935)
The asymptotic expansion of the generalized Bessel function,

Proc. London Math. Soc. (2) 38, pp. 257–270.

External Links:

Document, ZentralBlatt.

Referenced by:

§10.46.

Encodings:

BibTeX
E. M. Wright (1940a)
The asymptotic expansion of the generalized hypergeometric function,

Proc. London Math. Soc. (2) 46, pp. 389–408.

External Links:

ISSN 0024-6115, Document, MathReview (M. C. Gray), ZentralBlatt.

Referenced by:

§16.11(ii).

Encodings:

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E. M. Wright (1940b)
The generalized Bessel function of order greater than one,

Quart. J. Math., Oxford Ser. 11, pp. 36–48.

External Links:

Document, MathReview (M. C. Gray), ZentralBlatt.

Referenced by:

§10.46.

Encodings:

BibTeX
F. J. Wright (1980)
The Stokes set of the cusp diffraction catastrophe,

J. Phys. A 13 (9), pp. 2913–2928.

External Links:

ISSN 0305-4470, Document, MathReview (I. Stewart), ZentralBlatt.

Referenced by:

§36.5(ii).

Encodings:

BibTeX
C. Y. Wu (1982)
A series of inequalities for Mills’s ratio,

Acta Math. Sinica 25 (6), pp. 660–670.

External Links:

MathReview (J. S. Huang), ZentralBlatt.

Referenced by:

§7.8.

Encodings:

BibTeX
P. Wynn (1966)
Upon systems of recursions which obtain among the quotients of the Padé table,

Numer. Math. 8 (3), pp. 264–269.

External Links:

ISSN 0029-599X, Document, MathReview (F. L. Bauer), ZentralBlatt.

Referenced by:

§3.11(iv).

Encodings:

BibTeX