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, MOHAMMAD IDRIS and MALIK, SHAKIR HUSSAIN
(2021)
"A general double series identity and its application in hypergeometric reduction formulas,"
Turkish Journal of Mathematics: Vol. 45:
No.
6, Article 25.
https://doi.org/10.3906/mat-2105-101
Available at:
https://journals.tubitak.gov.tr/math/vol45/iss6/25
