Application of finite-part integration in the evaluation of the generalized Stieltjes transform

Abstract

The generalized Stieltjes transform is evaluated by the method of finite-part integration, and the result is compared with the results of the two most popular computer algebra systems, Maple and Mathematica. It is found that the integrators and the differential equation solvers of the computer algebra systems yield erroneous results under certain values of the parameters of the generalized Stieltjes transform.