Some hypergeometric summation theorems and reduction formulas via Laplace transform method

M. I. Qureshi; Showkat Ahmad Dar

paper

Some hypergeometric summation theorems and reduction formulas via Laplace transform method

arXiv:1808.06522

Abstract

In this paper, we obtain analytical solutions of Laplace transform based some generalized class of the hyperbolic integrals in terms of hypergeometric functions $_{3} F_{2} (\pm 1)$ , $_{4} F_{3} (\pm 1)$ , $_{5} F_{4} (\pm 1)$ , $_{6} F_{5} (\pm 1)$ , $_{7} F_{6} (\pm 1)$ and $_{8} F_{7} (\pm 1)$ with suitable convergence conditions, by using some algebraic properties of Pochhammer symbols. In addition, reduction formulas for $_{4} F_{3} (1)$ , $_{7} F_{6} (- 1)$ and some new summation theorems (not recorded earlier in the literature of hypergeometric functions) for $_{3} F_{2} (- 1)$ , $_{6} F_{5} (\pm 1)$ , $_{7} F_{6} (\pm 1)$ and $_{8} F_{7} (\pm 1)$ are obtained.

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