An alternative proof of the extended Saalschütz summation theorem for the r + 3Fr + 2(1) series with applications

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

Research output: Contribution to journalArticle

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Abstract

A simple proof is given of a new summation formula recently added in the literature for a terminating r + 3Fr + 2(1) hypergeometric series for the case when r pairs of numeratorial and denominatorial parameters differ by positive integers. This formula represents an extension of the well-known Saalschütz summation formula for a 3F2(1) series. Two applications of this extended summation formula are discussed. The first application extends two identities given by Ramanujan and the second, which also employs a similar extension of the Vandermonde–Chu summation theorem for the 2F1 series, extends certain reduction formulas for the Kampé de Fériet function of two variables given by Exton and Cvijović & Miller.
Original languageEnglish
Pages (from-to)4891-4900
Number of pages10
JournalMathematical Methods in the Applied Sciences
Volume38
Issue number18
Early online date6 Mar 2015
DOIs
Publication statusPublished - Dec 2015

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Summation Formula
Summation
Series
Alternatives
Theorem
Reduction formula
Hypergeometric Series
Ramanujan
Integer

Cite this

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abstract = "A simple proof is given of a new summation formula recently added in the literature for a terminating r + 3Fr + 2(1) hypergeometric series for the case when r pairs of numeratorial and denominatorial parameters differ by positive integers. This formula represents an extension of the well-known Saalsch{\"u}tz summation formula for a 3F2(1) series. Two applications of this extended summation formula are discussed. The first application extends two identities given by Ramanujan and the second, which also employs a similar extension of the Vandermonde–Chu summation theorem for the 2F1 series, extends certain reduction formulas for the Kamp{\'e} de F{\'e}riet function of two variables given by Exton and Cvijović & Miller.",
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An alternative proof of the extended Saalschütz summation theorem for the r + 3Fr + 2(1) series with applications. / Kim, Yong S.; Rathie, Arjun K.; Paris, Richard B.

In: Mathematical Methods in the Applied Sciences, Vol. 38, No. 18, 12.2015, p. 4891-4900.

Research output: Contribution to journalArticle

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