Topics in special functions

TL;DR

This paper addresses the connection problem of Hermite polynomials with other classical orthogonal polynomials in the Askey scheme using hypergeometric functions, building on prior work by Fields and Ismail.

Contribution

It introduces a new method combining hypergeometric functions to solve the connection problem for Hermite polynomials with Askey scheme polynomials.

Findings

Established explicit connection formulas for Hermite and other orthogonal polynomials

Extended the hypergeometric functions approach to a broader class of polynomials

Provided insights into the structure of special functions in the Askey scheme

Abstract

In this article, we solve the connection problem of the Hermite polynomials with the classical continuous orthogonal polynomials belonging to Askey scheme, using the hypergeometric functions method combined is with the work the Fields and Ismail.