Definite Integrals using Orthogonality and Integral Transforms

TL;DR

This paper derives new definite integrals involving associated Legendre functions, Bessel functions, and Chebyshev polynomials by leveraging orthogonality properties and integral transforms.

Contribution

It introduces novel integral formulas connecting special functions through orthogonality and integral transform techniques.

Findings

Derived new integral formulas for special functions.

Connected Legendre, Bessel, and Chebyshev functions via integrals.

Enhanced methods for evaluating definite integrals of special functions.

Abstract

We obtain definite integrals for products of associated Legendre functions with Bessel functions, associated Legendre functions, and Chebyshev polynomials of the first kind using orthogonality and integral transforms.