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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title = "An extension of Saalsch{\"u}tz's summation theorem for the series r+3Fr+2",

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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AU - Rathie, Arjun K.

AU - Paris, Richard B.

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N2 - 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].

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].

U2 - 10.1080/10652469.2013.777721

DO - 10.1080/10652469.2013.777721

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JO - Integral Transforms and Special Functions

JF - Integral Transforms and Special Functions

SN - 1065-2469

IS - 11

ER -

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

Abstract

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