Integral operators involving Whittaker functions

Abstract

We define the integral operators and asandwhereand Wk, u and Mk, u are the Whittaker's confluent hyper-geometric functions. These operators, in their slightly less general form, have been dealt with in [2] and [4]. There the authors have used the fact that these integral operators can be expressed as compositions of the Kober's fractional integral operators and the modified Laplace operator. Then these operators are inverted accordingly. Generally, this type of technique has been very useful for inverting many kinds of integral equations; and a good account of the procedures involved is given [5].