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
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
Copyright © 1994 Nanigopal Mandal and B. N. Mandal. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.