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This article is cited in 3 scientific papers (total in 3 papers)
Real, complex and functional analysis
New identities for a sum of products of the Kummer functions
S. I. Kalmykovab, D. B. Karpab a Institute of Applied Mathematics, FEBRAS,
7 Radio St.,
690041, Vladivostok, Russia
b Far Eastern Federal University,
8 Sukhanova St.,
690090, Vladivostok, Russia
Abstract:
In this note we present a summation formula for the Clausen series ${}_3F_{2}(1)$ with two integral parameter differences of opposite sign and apply it to give a generalization of a particular case of a very general reduction formula for a sum of products of the generalized hypergeometric functions discovered recently by Feng, Kuznetsov and Yang (J. Math. Anal. Appl. 443(2016), 116–122). Our generalization pertains to the case when the generalized hypergeometric function is reduced to the Kummer function ${}_1F_1$ and contains an additional integer shift in the bottom parameter of the Kummer function.
In the ultimate section of the paper we prove another formula for a particular product difference of the Kummer functions in terms of a linear combination of these functions.
Keywords:
Kummer function, Clausen function, hypergeometric identity, summation theorem, duality relations for hypergeometric functions.
Received November 11, 2017, published March 19, 2018
Citation:
S. I. Kalmykov, D. B. Karp, “New identities for a sum of products of the Kummer functions”, Sib. Èlektron. Mat. Izv., 15 (2018), 267–276
Linking options:
https://www.mathnet.ru/eng/semr916 https://www.mathnet.ru/eng/semr/v15/p267
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