ON A NEW CLASS OF SERIES IDENTITIES

• Journal title : Honam Mathematical Journal
• Volume 37, Issue 3,  2015, pp.339-352
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2015.37.3.339
Title & Authors
ON A NEW CLASS OF SERIES IDENTITIES
SHEKHAWAT, NIDHI; CHOI, JUNESANG; RATHIE, ARJUN K.; PRAKASH, OM;

Abstract
We aim at giving explicit expressions of $\small{{\sum_{m,n=0}^{{\infty}}}{\frac{{\Delta}_{m+n}(-1)^nx^{m+n}}{({\rho})_m({\rho}+i)_nm!n!}}$, where i = 0, $\small{{\pm}1}$, $\small{{\ldots}}$, $\small{{\pm}9}$ and $\small{\{{\Delta}_n\}}$ is a bounded sequence of complex numbers. The main result is derived with the help of the generalized Kummer's summation theorem for the series $\small{_2F_1}$ obtained earlier by Choi. Further some special cases of the main result considered here are shown to include the results obtained earlier by Kim and Rathie and the identity due to Bailey.
Keywords
Gamma function;Pochhammer symbol;Hypergeometric function;Generalized hypergeometric function;Generalized Kummer's summation theorem;
Language
English
Cited by
References
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