Extension of some classical summation theorems for the generalized hypergeometric series with integral parameter differences

DOI10.7153/jca-03-10zbMath1412.33013OpenAlexW2566710932MaRDI QIDQ3120707

Arjun K. Rathie, Richard B. Paris

Publication date: 5 March 2019

Published in: Journal of Classical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.7153/jca-03-10

zbMATH Keywords

generalized hypergeometric seriesgeneralized Gauss and Kummer summation theoremsgeneralized Watson summation theorem

Mathematics Subject Classification ID

Generalized hypergeometric series, ({}_pF_q) (33C20) Confluent hypergeometric functions, Whittaker functions, ({}_1F_1) (33C15)

Related Items (3)

The Clausenian hypergeometric function \({}_3 F_2\) with unit argument and negative integral parameter differences ⋮ New properties of a certain method of summation of generalized hypergeometric series ⋮ Some summation theorems for Clausen's hypergeometric functions with unit argument

Cites Work

• Extensions of certain classical summation theorems for the series \(_2F_1\), \(_3F_2\) and with applications in Ramanujan's summations
• Euler-type transformations for the generalized hypergeometric function \(_{r+2} F _{r+1}(x)\)
• Generalizations of Whipple's theorem on the sum of a \({}_ 3 F_ 2\)
• Transformation formulas for the generalized hypergeometric function with integral parameter differences
• Certain summation and transformation formulas for generalized hypergeometric series
• An extension of Saalschütz's summation theorem for the series_r+3F_r+2
• Certain transformations and summations for generalized hypergeometric series with integral parameter differences
• Generalizations of classical summation theorems for the series₂F₁and₃F₂with applications
• A generalization of a formula due to Kummer^†
• P-symbols, Heun Identities, and 3F2 Identities
• Karlsson–Minton summation theorems for the generalized hypergeometric series of unit argument
• Generalizations of Dixon's Theorem on the Sum of A 3 F 2
• Hypergeometric Functions with Integral Parameter Differences
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