A Probabilistic proof of some integral formulas involving the Meijer $G$-function

TL;DR

This paper derives new integral formulas involving the Meijer G-function by applying recent probabilistic distributional characterisations and transformations.

Contribution

It introduces a probabilistic approach to derive integral formulas for the Meijer G-function, expanding the analytical tools available for this special function.

Findings

New integral formulas involving the Meijer G-function are established.

Probabilistic methods are effectively applied to derive complex integral identities.

The results enhance understanding of the Meijer G-function's properties and applications.

Abstract

New integral formulas involving the Meijer $G$-function are derived using recent results concerning distributional characterisations and distributional transformations in probability theory.