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

Title & Authors
A SUMMATION FORMULA FOR THE SERIES 3F2 DUE TO FOX AND ITS GENERALIZATIONS
Choi, Junesang; Rathie, Arjun K.;

Abstract
Fox [2] presented an interesting identity for $\small{_pF_q}$ which is expressed in terms of a finite summation of $\small{_pF_q}$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 $\small{_3F_2(1/2)}$ as a special case of his above-mentioned general identity with the help of Kummers second summation theorem for $\small{_2F_1(1/2)}$. Here, in this paper, we show how two general summation formulas for $\small{_3F_2$\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 Foxs general identity with, here, the aid of generalizations of Kummers second summation theorem for $\small{_2F_1(1/2)}$ 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;Kummers second summation theorem;Foxs identity;
Language
English
Cited by
References
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