Euler-type transformations for the generalized hypergeometric function \(_{r+2} F _{r+1}(x)\)

DOI10.1007/s00033-010-0085-0zbMath1225.33005OpenAlexW1976149960WikidataQ56267216 ScholiaQ56267216MaRDI QIDQ638652

Allen R. Miller, Richard B. Paris

Publication date: 13 September 2011

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00033-010-0085-0

zbMATH Keywords

generalized hypergeometric functionEuler transformationKummer transformation

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) Confluent hypergeometric functions, Whittaker functions, ({}_1F_1) (33C15)

Related Items (14)

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Cites Work

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• Transformations of Kummer-type for \(_2F_2\)-series and their \(q\)-analogues
• On the reducibility of the Kampé de Fériet function
• On a Kummer-type transformation for the generalized hypergeometric function \(_{2}F_{2}\)
• A Kummer-type transformation for a \(_{2}F_{2}\) hypergeometric function
• Transformation formulas for the generalized hypergeometric function with integral parameter differences
• Certain summation and transformation formulas for generalized hypergeometric series
• A Generalised Kummer-Type Transformation for the _pF_p(x) Hypergeometric Function
• P-symbols, Heun Identities, and 3F2 Identities
• Karlsson–Minton summation theorems for the generalized hypergeometric series of unit argument
• A summation formula for Clausen's series₃F₂(1) with an application to Goursat's function₂F₂(x)

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