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http://dx.doi.org/10.4134/CKMS.2015.30.2.103

A SUMMATION FORMULA FOR THE SERIES 3F2 DUE TO FOX AND ITS GENERALIZATIONS  

Choi, Junesang (Department of Mathematics Dongguk University)
Rathie, Arjun K. (Department of Mathematics School of Mathematical and Physical Sciences Central University of Kerala, Riverside Transit Campus)
Publication Information
Communications of the Korean Mathematical Society / v.30, no.2, 2015 , pp. 103-108 More about this Journal
Abstract
Fox [2] presented an interesting identity for $_pF_q$ which is expressed in terms of a finite summation of $_pF_q$'s whose involved numerator and denominator parameters are different from those in the starting one. Moreover Fox [2] found a very interesting and general summation formula for $_3F_2(1/2)$ as a special case of his above-mentioned general identity with the help of Kummer's second summation theorem for $_2F_1(1/2)$. Here, in this paper, we show how two general summation formulas for $$_3F_2\[\array{\hspace{110}{\alpha},{\beta},{\gamma};\\{\alpha}-m,\;\frac{1}{2}({\beta}+{\gamma}+i+1);}\;{\frac{1}{2}}\]$$, m being a nonnegative integer and i any integer, can be easily established by suitably specializing the above-mentioned Fox's general identity with, here, the aid of generalizations of Kummer's second summation theorem for $_2F_1(1/2)$ obtained recently by Rakha and Rathie [7]. Several known results are also seen to be certain special cases of our main identities.
Keywords
Gamma function; Pochhammer symbol; hypergeometric function; generalized hypergeometric function; Kummer's second summation theorem; Fox's identity;
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