• EXPANSION OF GENERAL CLASS OF FUNCTIONS IN TERMS OF GENERALIZED PROLATE SPHEROIDAL WAVE FUNCTION AND ITS APPLICATIONS

Abstract

The aim of the present paper is to establish an expansion formula for a general class of functions in terms of generalized prolate spheroidal wave function. For establishing this expansion formula an elementary integral has been evaluated first. The expansion formula being of very general nature can be transformed to yield many new results involving various commonly used functions, viz generalized hypergeometric function, Bessel function Riemann Zeta- function, Mittag-Leffler function etc., occurring in applied Mathematics and Mathematical Physics. For the sake of    illustration, some special cases of the expansion formula are mentioned. Finally, as applications of our result, expansions of Bernoulli¢s polynomial, H-function and Laguerre polynomial have been obtained.