Definite integrals from the finite parts of divergent Mellin-type pole singularity integrals involving entire functions

Abstract

New expressions for certain definite integrals are acquired from a structure of finite part integration. That is, applying the method of finite part integration on divergent Mellin-type pole singularity integrals with an entire function in the numerator yielded, within its complex contour integral representation, novel expressions for certain definite integrals. These integrals are notably both numerically verified and not tabulated in the literature, hence the utility of finite part integration is increased.