An alternative summation formula for the hypergeometric series p+2Fp+1(1) with integral parameter differences

R. B. Paris

doi:10.12988/ams.2021.916554

An alternative summation formula for the hypergeometric series p+2Fp+1(1) with integral parameter differences

R. B. Paris

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Abstract

We obtain a summation formula for the hypergeometric series of unit argument p+2Fp+1 with p pairs of numeratorial and denominatorial parameters differing by positive integers. This summation formula is an alternative representation to that presented by Miller and Paris [Rocky Mountain J. Math. 43 (1) (2013), 291{327] and involves a p-fold sum with coeffcients that contain only ratios of Pochhammer symbols. The case when one of the parameters is a negative integer is also considered.

Original language	English
Pages (from-to)	685-692
Number of pages	8
Journal	Applied Mathematical Sciences
Volume	15
Issue number	14
Early online date	25 Nov 2021
DOIs	https://doi.org/10.12988/ams.2021.916554
Publication status	Published - 25 Nov 2021

Keywords

Generalised hypergeometric function
Summation formulas at unit argument

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AB - We obtain a summation formula for the hypergeometric series of unit argument p+2Fp+1 with p pairs of numeratorial and denominatorial parameters differing by positive integers. This summation formula is an alternative representation to that presented by Miller and Paris [Rocky Mountain J. Math. 43 (1) (2013), 291{327] and involves a p-fold sum with coeffcients that contain only ratios of Pochhammer symbols. The case when one of the parameters is a negative integer is also considered.

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An alternative summation formula for the hypergeometric series p+2Fp+1(1) with integral parameter differences

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