Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

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Commun. Korean Math. Soc. 2012; 27(4): 745-751

Printed December 1, 2012

https://doi.org/10.4134/CKMS.2012.27.4.745

Copyright © The Korean Mathematical Society.

On sums of certain classes of series

Yong Sup Kim, Mahendra Pal Chaudhary, and Arjun Kumar Rathie

Wonkwang University, International Scientific Research and, Central University of Kerala

Abstract

The aim of this research note is to provide the sums of the series $$\sum_{k=0}^{\infty}(-1)^{k}\left(\begin{array}{lll} \,a-i\\ \,~~k\end{array} \right)\frac{1}{2^{k}(a+k+1)}$$ for $i=0,\pm{1}, \pm{2},\pm{3},\pm{4},\pm{5}$. The results are obtained with the help of generalization of Bailey's summation theorem on the sum of a ${}_{2}F_{1}$ obtained earlier by Lavoie et al.. Several interesting results including those obtained earlier by Srivastava, Vowe and Seiffert, follow special cases of our main findings. The results derived in this research note are simple, interesting, easily established and (potentially) useful.

Keywords: Bailey's summation theorem, summation theorems, gamma function

MSC numbers: Primary 33B15, 33C15, 39A10, 68Q40