New Laplace transforms for the generalized hypergeometric functions 2F2 and 3F3

TL;DR

This paper derives new Laplace transform formulas for generalized hypergeometric functions $_2F_2$ and $_3F_3$, extending previous results and employing advanced summation theorems.

Contribution

It introduces novel Laplace transforms for $_2F_2$ and $_3F_3$ hypergeometric functions using extended summation theorems, expanding the mathematical toolkit.

Findings

New Laplace transforms for $_2F_2$ and $__3F_3$ functions established.

Certain known results are recovered as special cases.

The methods extend classical summation theorems for hypergeometric series.

Abstract

Motivated by the new Laplace transforms for the Kummer's confluent hypergeometric functions $_1F_1$ obtained recently by Kim et al. [Math $\&$ Comput. Modelling, 55 (2012), pp. 1068--1071], the authors aim is to establish so far unknown Laplace transforms of rather general case of generalized hypergeometric functions $_2F_2(x)$ and $_3F_3(x)$ by employing extensions of classical summation theorems for the series $_2F_1$ and $_3F_2$ obtained recently by Kim et al. [Int. J. Math. Math. Sci., 309503, 26 pages, 2010]. Certain known results obtained earlier by Kim et al. follow cases of our main findings.