Expansion of a class of functions into an integral involving associated Legendre functions

Abstract

A theorem for expansion of a class of functions into an integral involving associated Legendre functions is obtained in this paper. This is a somewhat general integral expansion formula for a function f(x) defined in (x1,x2) where -1<x1<x2<1, which is perhaps useful in solving certain boundary value problems of mathematical physics and of elasticity involving conical boundaries.

Keywords

• integral expansion of a function
• associated Legendre function
• Mehler-Fok integral transform.