Laplace transform of some special functions in terms of generalized Meijer G-functions

Abstract

The aim of this paper is to prove Laplace transform of some special functions in term of generalized Meijer G-functions. Some properties of generalized Meijer G-functions will be discussed. We investigate the Laplace transform of different hypergeometric functions in the form of generalized Meijer G-functions and hypergeometric functions. We derive Laplace transform of Bessel k-functions, hyper-Bessel k-functions, incomplete gamma k-function, sine k-integral, sine hyperbolic k-integral, Kelvin k-function in the form of generalized Meijer G-functions. In fact, we provide new approach to find Laplace transform of said functions.

Certain Integral and Differential Formulas Involving the Product of Srivastava’s Polynomials and Extended Wright Function

“…Fractional calculus and integral transforms of general class of polynomials and incomplete Fox-Wright functions is discussed by Jangid et al [21]. Certain expressions of the Laguerre polynomial and relations of some known functions in terms of generalized Meijer G-functions are explored in [22,23].…”