Turkish Journal of Mathematics
DOI
10.3906/mat-2102-42
Abstract
We derive a summation formula for the terminating hypergeometric series \[{}_4F_3\left[\!\!\begin{array}{c}-m,a,b,1+c\\1+a+m,1+a-b,c\end{array}\!\!;1\right],\] where $m$ denotes a nonnegative integer. Using this summation formula, we establish a reduction formula for the Srivastava-Daoust double hypergeometric function with arguments $z$ and $-z$. Special cases of this reduction formula lead to several reduction formulas for the hypergeometric functions ${}_{p+1}F_p$ with quadratic arguments when $p=2,3$ and 4 by employing series rearrangement techniques. A general double series identity involving a bounded sequence of arbitrary complex numbers is also given.
Keywords
Hypergeometric summation theorems, Srivastava-Daoust double hypergeometric function, bounded sequence, series rearrangement technique
First Page
1903
Last Page
1913
Recommended Citation
QURESHI, MOHAMMAD IDRIS; PARIS, RICHARD BRUCE; and MALIK, SHAKIR HUSSAIN
(2021)
"A contiguous extension of Dixon's theorem for a terminating ${}_4F_3(1)$ series with applications,"
Turkish Journal of Mathematics: Vol. 45:
No.
5, Article 2.
https://doi.org/10.3906/mat-2102-42
Available at:
https://journals.tubitak.gov.tr/math/vol45/iss5/2
