Dougall bilateral sum
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11: 4.27 Sums
§4.27 Sums
►For sums of trigonometric and inverse trigonometric functions see Gradshteyn and Ryzhik (2000, Chapter 1), Hansen (1975, §§14–42), Oberhettinger (1973), and Prudnikov et al. (1986a, Chapter 5).12: 4.11 Sums
§4.11 Sums
…13: 18.12 Generating Functions
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18.12.7
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18.12.8
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18.12.9
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18.12.10
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►See §18.18(vii) for Poisson kernels; these are special cases of bilateral generating functions.
14: 4.41 Sums
§4.41 Sums
►For sums of hyperbolic functions see Gradshteyn and Ryzhik (2000, Chapter 1), Hansen (1975, §43), Prudnikov et al. (1986a, §5.3), and Zucker (1979).15: 7.15 Sums
§7.15 Sums
►For sums involving the error function see Hansen (1975, p. 423) and Prudnikov et al. (1986b, vol. 2, pp. 650–651).16: 5.16 Sums
§5.16 Sums
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5.16.1
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►For further sums involving the psi function see Hansen (1975, pp. 360–367).
For sums of gamma functions see Andrews et al. (1999, Chapters 2 and 3) and §§15.2(i), 16.2.
►For related sums involving finite field analogs of the gamma and beta functions (Gauss and Jacobi sums) see Andrews et al. (1999, Chapter 1) and Terras (1999, pp. 90, 149).
17: 27.10 Periodic Number-Theoretic Functions
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►An example is Ramanujan’s sum:
…It can also be expressed in terms of the Möbius function as a divisor sum:
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►More generally, if and are arbitrary, then the sum
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►Another generalization of Ramanujan’s sum is the Gauss sum
associated with a Dirichlet character .
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is separable for some if
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18: 24.20 Tables
§24.20 Tables
►Abramowitz and Stegun (1964, Chapter 23) includes exact values of , , ; , , , , 20D; , , 18D. …19: 25.16 Mathematical Applications
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