•  
  •  
 

Turkish Journal of Mathematics

DOI

10.3906/mat-2105-101

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

First Page

2759

Last Page

2772

Download

Included in

Mathematics Commons

Share

COinS