Certain summation and transformation formulas for generalized hypergeometric series

DOI10.1016/j.cam.2009.05.013zbMath1221.33011OpenAlexW1992479047MaRDI QIDQ2271981

Allen R. Miller

Publication date: 5 August 2009

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

Full work available at URL: https://doi.org/10.1016/j.cam.2009.05.013

zbMATH Keywords

Kampé de Fériet functionshypergeometric reduction formulas

Mathematics Subject Classification ID

Generalized hypergeometric series, ({}_pF_q) (33C20) Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable (33C50)

Related Items (14)

A Kummer-type transformation for some k-hypergeometric functions ⋮ Fractional integral operators characterized by some new hypergeometric summation formulas ⋮ An alternative proof of the extended Saalschütz summation theorem for the _{r + 3} F _{r + 2} (1) series with applications ⋮ A contiguous extension of Dixon’s theorem for a terminating 4F3(1) series with applications ⋮ Euler-type transformations for the generalized hypergeometric function \(_{r+2} F _{r+1}(x)\) ⋮ Transformation formulas for the generalized hypergeometric function with integral parameter differences ⋮ ON A MULTIVARIABLE CLASS OF MITTAG-LEFFLER TYPE FUNCTIONS ⋮ Karlsson–Minton summation theorems for the generalized hypergeometric series of unit argument ⋮ Certain transformations and summations for generalized hypergeometric series with integral parameter differences ⋮ Unnamed Item ⋮ Some summation theorems for generalized hypergeometric functions ⋮ Generalization of two theorems due to Ramanujan ⋮ Extension of some classical summation theorems for the generalized hypergeometric series with integral parameter differences ⋮ Differentiation identities for hypergeometric functions

Cites Work

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• A Kummer-type transformation for a \(_{2}F_{2}\) hypergeometric function
• A summation formula for Clausen's series₃F₂(1) with an application to Goursat's function₂F₂(x)
• Generalized Hypergeometric Function of Unit Argument
• Hypergeometric Functions with Integral Parameter Differences

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