International Journal of Mathematics and Mathematical Sciences 
Volume 17 (1994), Issue 2, Pages 293-300
doi:10.1155/S0161171294000438

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

Nanigopal Mandal1 and B. N. Mandal2

 1Calcutta Mathematical Society, AE-374, Sector I, Salt Lake City, Calcutta 700 064, India
2Physical and Earth Science Division, Indian Statistical Institute, 203, B.T. Road, Calcutta 700 035, India
Received 4 February 1992; Revised 18 March 1993

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.