Some hypergeometric summation theorems and reduction formulas via Laplace transform method

M. I. Qureshi; Showkat Ahmad Dar

Some hypergeometric summation theorems and reduction formulas via Laplace transform method

Classical Analysis and ODEs 2018-08-21 v1

Authors: M. I. Qureshi , Showkat Ahmad Dar

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.

Keywords

hypergeometric functions hyperbolic geometry

Cite

@article{arxiv.1808.06522,
  title  = {Some hypergeometric summation theorems and reduction formulas via Laplace transform method},
  author = {M. I. Qureshi and Showkat Ahmad Dar},
  journal= {arXiv preprint arXiv:1808.06522},
  year   = {2018}
}

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21 pages, 0 figure

Some hypergeometric summation theorems and reduction formulas via Laplace transform method

Abstract

Keywords

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