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arXiv · 1808.06522

Some hypergeometric summation theorems and reduction formulas via Laplace transform method

M. I. Qureshi·Showkat Ahmad Dar
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Abstract

In this paper, we obtain analytical solutions of Laplace transform based some generalized class of the hyperbolic integrals in terms of hypergeometric functions ${}_3F_2 (\pm1)$, ${}_4F_3 (\pm1)$, ${}_5F_4(\pm1)$, ${}_6F_5(\pm1)$, ${}_7F_6(\pm1)$ and ${}_8F_7(\pm1)$ with suitable convergence conditions, by using some algebraic properties of Pochhammer symbols. In addition, reduction formulas for ${}_4F_3(1)$, ${}_7F_6(-1)$ and some new summation theorems (not recorded earlier in the literature of hypergeometric functions) for ${}_3F_2(-1)$, ${}_6F_5(\pm1)$, ${}_7F_6(\pm1)$ and ${}_8F_7(\pm1)$ are obtained.

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M. I. Qureshi, Showkat Ahmad Dar. 2018-08-17. Some hypergeometric summation theorems and reduction formulas via Laplace transform method. https://arxiv.org/abs/1808.06522

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