Generalized Watson's summation formula for \(_3F_2(1)\)

DOI10.1016/S0377-0427(97)00170-2zbMath0903.33004MaRDI QIDQ1379013

Stanisław Lewanowicz

Publication date: 1997

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

Watson's summation formula

Mathematics Subject Classification ID

Generalized hypergeometric series, ({}_pF_q) (33C20)

Related Items (17)

The Clausenian hypergeometric function \({}_3 F_2\) with unit argument and negative integral parameter differences ⋮ Unnamed Item ⋮ Another class of nonterminating \(_3F_2\)-series with a free argument ⋮ M. Jackson's bilateral \(_{3} H _{3}\)-series and extension with integer parameters ⋮ Nonterminating ₃F₂-series with a free variable ⋮ Generalization of a quadratic transformation formula due to Gauss ⋮ Applications of extended Watson's summation theorem ⋮ Non-terminating₃F₂-series with unit argument ⋮ Unnamed Item ⋮ Asymptotic expansion of a Bessel function integral using hypergeometric functions ⋮ Extensions of the classical theorems for very well-poised hypergeometric functions ⋮ Terminating balanced \(_{4}F_{3}\)-series and very well-poised \(_{7}F_{6}\)-series ⋮ Generalizations of classical summation theorems for the series₂F₁and₃F₂with applications ⋮ Bootstrapping quantum extremal surfaces. I: The area operator ⋮ Analytical formulae for extended $_{3}F_{2}$-series of Watson–Whipple–Dixon with two extra integer parameters ⋮ Generalizations of a formula due to Kummer with applications ⋮ Some summation theorems for Clausen's hypergeometric functions with unit argument

Uses Software

• Maple

Cites Work

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• Irreducible recurrences and representation theorems for \(_ 3F_ 2(1)\)
• Gauss's \(_ 2F_ 1(1)\) cannot be generalized to \(_ 2F_ 1(x)\)
• Some remarks on uniform asymptotic expansions for Bessel functions
• Generalizations of Whipple's theorem on the sum of a \({}_ 3 F_ 2\)
• Notes on a paper by J. B. Miller
• Some Summation Formulas for the Series 3 F 2 (1)
• Generalizations of Dixon's Theorem on the Sum of A 3 F 2
• Generating Functions for Bessel and Related Polynomials
• Contiguous Hypergeometric Functions of the Type ₃F₂(1)

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