A Note on Integrals Containing the Univariate Lommel Function

TL;DR

This paper explores integrals involving the univariate Lommel function and reveals a new relationship between these integrals and Chebyshev polynomials, contributing to special functions theory.

Contribution

It uncovers a novel integral relationship connecting Lommel functions with Chebyshev polynomials, expanding understanding of their interconnections.

Findings

Derived new integral relationship involving Lommel functions and Chebyshev polynomials

Identified specific integral formulas linking these special functions

Enhanced theoretical understanding of special functions' interrelations

Abstract

This short note investigates a number of index integrals of products of the Lommel functions $s_{\mu,\nu}(a)$ and uncovers an integral relationship. between this function and the Tchebyshev polynomials $T_{2n}(x)$.