An extension of Saalschütz's summation theorem for the series r+3Fr+2

Yong S. Kim; Arjun K. Rathie; Richard B. Paris

doi:10.1080/10652469.2013.777721

An extension of Saalschütz's summation theorem for the series _r+3F_r+2

Yong S. Kim, Arjun K. Rathie, Richard B. Paris

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Abstract

The aim in this research note is to provide an extension of Saalschütz's summation theorem for the series _r+3F_r+2(1) when r pairs of numeratorial and denominatorial parameters differ by positive integers. The result is obtained by exploiting a generalization of an Euler-type transformation recently derived by Miller and Paris [Transformation formulas for the generalized hypergeometric function with integral parameter differences. Rocky Mountain J Math. 2013;43, to appear].

Original language	English
Pages (from-to)	916-921
Number of pages	6
Journal	Integral Transforms and Special Functions
Volume	24
Issue number	11
Early online date	16 May 2013
DOIs	https://doi.org/10.1080/10652469.2013.777721
Publication status	Published - 2013

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Kim, Y. S., Rathie, A. K., & Paris, R. B. (2013). An extension of Saalschütz's summation theorem for the series _r+3F_r+2. Integral Transforms and Special Functions, 24(11), 916-921. https://doi.org/10.1080/10652469.2013.777721

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abstract = "The aim in this research note is to provide an extension of Saalsch{\"u}tz's summation theorem for the series r+3Fr+2(1) when r pairs of numeratorial and denominatorial parameters differ by positive integers. The result is obtained by exploiting a generalization of an Euler-type transformation recently derived by Miller and Paris [Transformation formulas for the generalized hypergeometric function with integral parameter differences. Rocky Mountain J Math. 2013;43, to appear].",

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AB - The aim in this research note is to provide an extension of Saalschütz's summation theorem for the series r+3Fr+2(1) when r pairs of numeratorial and denominatorial parameters differ by positive integers. The result is obtained by exploiting a generalization of an Euler-type transformation recently derived by Miller and Paris [Transformation formulas for the generalized hypergeometric function with integral parameter differences. Rocky Mountain J Math. 2013;43, to appear].

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Access to Document

10.1080/10652469.2013.777721

Paris_AnExtinsionOfSaalschutz'sSummation_Author_2013Accepted author manuscript, 309 KB