A New Generating Function for Hermite Polynomials

TL;DR

This paper introduces a novel generating function for Hermite polynomials, linking it to the incomplete gamma function, which could enhance analytical and computational techniques involving these polynomials.

Contribution

The paper proposes a new generating function for Hermite polynomials and establishes its connection with the incomplete gamma function, offering a fresh perspective and potential tools for mathematical analysis.

Findings

New generating function for Hermite polynomials introduced

Connection established between the generating function and incomplete gamma function

Potential applications in mathematical analysis and computation

Abstract

This paper presents a new generating function for Hermite polynomials of one variable in the form of $g(x,t)=\sum_{n=0}^{\infty }t^{n}H^{e}_{n}(x)$ and reveals its connection with incomplete gamma function.