Integral representations for a generalized Hermite linear functional

TL;DR

This paper derives new integral representations for the generalized Hermite linear functional on the real line and complex plane, and applies these results to obtain novel integral representations of the Euler Gamma function.

Contribution

It introduces new integral representations for the generalized Hermite linear functional and the Euler Gamma function, expanding the analytical tools available for these functions.

Findings

New integral representations for the generalized Hermite linear functional

Novel integral formulas for the Euler Gamma function

Extensions to both real line and complex plane

Abstract

In this paper, we find new integral representations for the generalized Hermite linear functional in the real line and the complex plane. As an application, new integral representations for the Euler Gamma function are given.