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Sib. Èlektron. Mat. Izv., 2018, Volume 15, Pages 267–276 (Mi semr916)  

This article is cited in 1 scientific paper (total in 1 paper)

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.

Funding Agency Grant Number
Russian Science Foundation 14-11-00022
This research has been supported by the Russian Science Foundation under project 14-11-00022.


DOI: https://doi.org/10.17377/semi.2018.15.025

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Bibliographic databases:

Document Type: Article
UDC: 517.588
MSC: 33C15, 33C20
Received November 11, 2017, published March 19, 2018
Language: English

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

Citation in format AMSBIB
\Bibitem{KalKar18}
\by S.~I.~Kalmykov, D.~B.~Karp
\paper New identities for a sum of products of the Kummer functions
\jour Sib. \`Elektron. Mat. Izv.
\yr 2018
\vol 15
\pages 267--276
\mathnet{http://mi.mathnet.ru/semr916}
\crossref{https://doi.org/10.17377/semi.2018.15.025}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000438412200025}


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  • http://mi.mathnet.ru/eng/semr/v15/p267

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. I. Kalmykov, D. B. Karp, “Inequalities for some basic hypergeometric functions”, Probl. anal. Issues Anal., 8(26):1 (2019), 47–64  mathnet  crossref
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