Numerical inversion of Mellin transforms

A method is presented for the numerical inversion of Mellin transforms in which the inverse is obtained as an expansion in terms of Laguerre polynomials. The coefficients of this expansion are obtained as linear combinations of values of the transformed function or, equivalently, in terms of forward differences of this function. Thus, the Mellin transform of the series can be written as a forward interpolation series. Consequently the error of the numerical inversion procedure can be estimated. The practical advantage of the method is that values are needed for real arguments only.