Turkish Journal of Mathematics
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.
DOI
10.3906/mat-2105-101
Keywords
Srivastava-Daoust double hypergeometric function, hypergeometric summation theorem, hypergeometric transformation and reduction formula, bounded sequence, series rearrangement technique
First Page
2759
Last Page
2772
Recommended Citation
QURESHI, M. I, & MALIK, S. H (2021). A general double series identity and its application in hypergeometric reduction formulas. Turkish Journal of Mathematics 45 (6): 2759-2772. https://doi.org/10.3906/mat-2105-101
