Geodesic
New identities for a sum of products of the Kummer functions
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 267-276

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{SEMR_2018_15_a124,
     author = {S. I. Kalmykov and D. B. Karp},
     title = {New identities for a sum of products of the {Kummer} functions},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {267--276},
     publisher = {mathdoc},
     volume = {15},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2018_15_a124/}
}
TY  - JOUR
AU  - S. I. Kalmykov
AU  - D. B. Karp
TI  - New identities for a sum of products of the Kummer functions
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2018
SP  - 267
EP  - 276
VL  - 15
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2018_15_a124/
LA  - en
ID  - SEMR_2018_15_a124
ER  - 
%0 Journal Article
%A S. I. Kalmykov
%A D. B. Karp
%T New identities for a sum of products of the Kummer functions
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2018
%P 267-276
%V 15
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2018_15_a124/
%G en
%F SEMR_2018_15_a124
S. I. Kalmykov; D. B. Karp. New identities for a sum of products of the Kummer functions. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 267-276. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a124/