Poisson%20kernels
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21: 10.73 Physical Applications
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►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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22: 8.26 Tables
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Khamis (1965) tabulates for , to 10D.
Abramowitz and Stegun (1964, pp. 245–248) tabulates for , to 7D; also for , to 6S.
Pagurova (1961) tabulates for , to 4-9S; for , to 7D; for , to 7S or 7D.
Zhang and Jin (1996, Table 19.1) tabulates for , to 7D or 8S.
23: 23 Weierstrass Elliptic and Modular
Functions
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24: 10.63 Recurrence Relations and Derivatives
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►Equations (10.63.6) and (10.63.7) also hold when the symbols and in (10.63.5) are replaced throughout by and , respectively.
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§10.63(i) , , ,
… ►25: 12.16 Mathematical Applications
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►PCFs are also used in integral transforms with respect to the parameter, and inversion formulas exist for kernels containing PCFs.
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26: 1.9 Calculus of a Complex Variable
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Poisson Integral
…27: 36 Integrals with Coalescing Saddles
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28: Gergő Nemes
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►As of September 20, 2021, Nemes performed a complete analysis and acted as main consultant for the update of the source citation and proof metadata for every formula in Chapter 25 Zeta and Related Functions.
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29: Wolter Groenevelt
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►As of September 20, 2022, Groenevelt performed a complete analysis and acted as main consultant for the update of the source citation and proof metadata for every formula in Chapter 18 Orthogonal Polynomials.
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