A Class of Integral Transforms

Abstract

In this paper we discuss a new class of integral transforms and their inversion formula. The kernel in the transform is a G -function (for a treatment of this function, see (( 1 ), 5.3) and integration is performed with respect to the argument of that function. In the inversion formula, the kernel is likewise a G -function, but there integration is performed with respect to a parameter. Known special cases of our results are the Kontorovitch-Lebedev transform pair (( 2 ), v. 2; ( 3 )) and the generalised Mehler transform pair (7) These transforms are used in solving certain boundary value problems of the wave or heat conduction equation involving wedge or conically-shaped boundaries, and are extensively tabulated in ( 6 ).