Authors: MOHAMMAD IDRIS QURESHI, SHAKIR HUSSAIN MALIK

Abstract: In this paper, we obtain a general double-series identity involving the bounded sequence of arbitrary complex numbers. As application of our double-series identity, we establish some reduction formulas for Srivastava--Daoust double hypergeometric function and Gaussian generalized hypergeometric function $_4F_3$. As special cases of our reduction formula for $_4F_3$ lead to some corollaries involving Clausen hypergeometric functions ${_{3}F_{2}}$. Making suitable adjustment of parameters in reduction formulas for $_4F_3$ and ${_{3}F_{2}}$, we obtain some results in terms of elementary functions and some special functions like Lerch generalized zeta function and incomplete beta function.

Keywords: Srivastava-Daoust double hypergeometric function, hypergeometric summation theorem, hypergeometric transformation and reduction formula, bounded sequence, series rearrangement technique

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