Evaluation of a class of integrals occurring in mathematical physics via a higher order generalization of the principal value

Abstract

The notion of the principal value of an integral is generalized to treat higher order singularities. The principal value of an integral can be considered the "convergent part" of a divergent integral, an interpretation that is almost trivial for simple poles, but more meaningful for higher order poles. Application of this concept leads to a simple algorithm that may be applied to the evaluation of a class of integrals arising in mathematical physics. Many of these integrals frequently occur in the analytic and numerical evaluation of folding functions arising from the product of single-particle Green's functions.