A numerical method of computing Hadamard finite-part integrals with an integral power singularity at the endpoint on a half infinite interval

Abstract: In this paper, we propose a numerical method of computing Hadamard finite-part integrals with an integral power singularity at the endpoint on a half infinite interval, that is, a finite value assigned to a divergent integral with an integral power singularity at the endpoint on a half infinite interval. In the proposed method, we express a desired finite-part integral using a complex integral, and we obtain the integral by evaluating the complex integral by the DE formula. Theoretical error estimate and some numerical examples show the effectiveness of the proposed method.