Dougall%20bilateral%20sum
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1: 16.4 Argument Unity
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Rogers–Dougall Very Well-Poised Sum
… ►Dougall’s Very Well-Poised Sum
… ►Denote, formally, the bilateral hypergeometric function …This is Dougall’s bilateral sum; see Andrews et al. (1999, §2.8).2: 20 Theta Functions
Chapter 20 Theta Functions
…3: 14.18 Sums
§14.18 Sums
… ►§14.18(iii) Other Sums
… ►Dougall’s Expansion
… ►For collections of sums involving associated Legendre functions, see Hansen (1975, pp. 367–377, 457–460, and 475), Erdélyi et al. (1953a, §3.10), Gradshteyn and Ryzhik (2000, §8.92), Magnus et al. (1966, pp. 178–184), and Prudnikov et al. (1990, §§5.2, 6.5). …4: 15.4 Special Cases
5: Bibliography D
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Recherches analytiques sur la théorie des nombres premiers. Première partie. La fonction de Riemann et les nombres premiers en général, suivi d’un Appendice sur des réflexions applicables à une formule donnée par Riemann.
Ann. Soc. Sci. Bruxelles 20, pp. 183–256 (French).
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Recherches analytiques sur la théorie des nombres premiers. Deuxième partie. Les fonctions de Dirichlet et les nombres premiers de la forme linéaire
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Ann. Soc. Sci. Bruxelles 20, pp. 281–397 (French).
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Complex zeros of cylinder functions.
Math. Comp. 20 (94), pp. 215–222.
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On Vandermonde’s theorem, and some more general expansions.
Proc. Edinburgh Math. Soc. 25, pp. 114–132.
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Uniform asymptotic expansions for Whittaker’s confluent hypergeometric functions.
SIAM J. Math. Anal. 20 (3), pp. 744–760.
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6: 8 Incomplete Gamma and Related
Functions
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7: 28 Mathieu Functions and Hill’s Equation
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8: 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.
9: 23 Weierstrass Elliptic and Modular
Functions
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