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1: 13 Confluent Hypergeometric Functions
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2: 16 Generalized Hypergeometric Functions & Meijer G-Function
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3: 13.30 Tables
§13.30 Tables
… ►Slater (1960) tabulates for , , and , 7–9S; for and , 7D; the smallest positive -zero of for and , 7D.
4: 24.20 Tables
§24.20 Tables
… ►In Wagstaff (2002) these results are extended to and , respectively, with further complete and partial factorizations listed up to and , respectively. ►For information on tables published before 1961 see Fletcher et al. (1962, v. 1, §4) and Lebedev and Fedorova (1960, Chapters 11 and 14).5: 17 q-Hypergeometric and Related Functions
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6: 10.73 Physical Applications
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►See Jackson (1999, Chapter 9, §9.6), Jones (1986, Chapters 7, 8), and Lord Rayleigh (1945, Vol. I, Chapter IX, §§200–211, 218, 219, 221a;
Vol. II, Chapter XIII, §272a; Chapter XV, §302; Chapter XVIII;
Chapter XIX, §350; Chapter XX, §357;
Chapter XXI, §369).
…Consequently, Bessel functions , and modified Bessel functions , are central to the analysis of microwave and optical transmission in waveguides, including coaxial and fiber.
See Krivoshlykov (1994, Chapter 2, §2.2.10; Chapter 5, §5.2.2), Kapany and Burke (1972, Chapters 4–6; Chapter 7, §A.1), and Slater (1942, Chapter 4, §§20, 25).
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►The analysis of the current distribution in circular conductors leads to the Kelvin functions , , , and .
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►For applications of the Rayleigh function (§10.21(xiii)) to problems of heat conduction and diffusion in liquids see Kapitsa (1951a).
7: 15 Hypergeometric Function
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8: 13.11 Series
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13.11.3
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9: Bibliography W
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Two tables of partitions.
Proc. London Math. Soc. (2) 42, pp. 550–556.
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A table of Ramanujan’s function
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Proc. London Math. Soc. (2) 51, pp. 1–13.
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Hill’s equation with a large potential.
SIAM J. Appl. Math. 45 (2), pp. 200–214.
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Tables of Summable Series and Integrals Involving Bessel Functions.
Holden-Day, San Francisco, CA.
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On the zeros of a confluent hypergeometric function.
Proc. Amer. Math. Soc. 16 (2), pp. 281–283.
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10: Bibliography K
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Auxiliary table for the incomplete elliptic integrals.
J. Math. Physics 27, pp. 11–36.
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The Hahn polynomials, formulas and an application.
Scripta Math. 26, pp. 33–46.
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Tables of values of the modified Mathieu functions.
Math. Comp. 14, pp. 118–129.
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Approximation Formulae for Generalized Hypergeometric Functions for Large Values of the Parameters.
J. B. Wolters, Groningen.
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Zeros of exceptional Hermite polynomials.
J. Approx. Theory 200, pp. 28–39.
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