The generalized Stieltjes transform and its inverse

Schwarz J.H.

The generalized Stieltjes transform (GST) is an integral transform that depends ona parameter r.0. In previous work a convenient form of the inverse transformationwas derived for the case r =3/2. This paper generalizes that result to all r.0. It is a well-known fact that the GST can be formulated as an iterated Laplacetransform, and that therefore its inverse can be expressed as an iterated inverseLaplace transform. The form of the inverse transform derived here is a onedimensionalintegral that is considerably simpler.