On integral equations involving Whittaker's function

Abstract

Recently some inversion integrals for integral equations involving Legendre, Chebyshev, Gegenbauer and Laguerre polynomials in the kernel have been obtained [1, 2, 3, 5, 6]. In this note, two inversion integrals for integral equations involving Whittaker's function in the kernel are obtained. We shall make use of the following known integral [4, p. 402]The results of this note are based on the following two integrals, which are derived from (1) by writing u – t = (v – t)x.for m + 1 > 2v > – 1;for m + 1 > 2v > – 1.