On a double integral of a product of Legendre polynomials

TL;DR

This paper derives a formula for a specific double integral involving Legendre polynomials and a binomial term raised to a power, expanding the analytical tools available for such integrals.

Contribution

The paper provides a new explicit calculation for a double integral of Legendre polynomial products with a binomial factor, which was previously unresolved.

Findings

Derived a closed-form expression for the integral

Extended the understanding of Legendre polynomial integrals

Potential applications in mathematical physics and approximation theory

Abstract

We calculate a double integral over a product of Legendre polynomials multiplied by a binomial raised to a power.