A Recursive Method for Computing Certain Bessel Function Integrals

TL;DR

This paper introduces a recursive approach to evaluate integrals involving modified Bessel functions, providing exact results through finite asymptotic expansions and applicable to similar integral families.

Contribution

It develops a recursive method for computing Bessel function integrals and establishes conditions for finite asymptotic expansions, advancing analytical techniques in this area.

Findings

Recursive formulas for Bessel integrals derived

Asymptotic expansions can be exact after finite terms

Bounds established for the termination of expansions

Abstract

We investigate a family of integrals involving modified Bessel functions that arise in the context of neutrino scattering. Recursive formulas are derived for evaluating these integrals and their asymptotic expansions are computed. We prove in certain cases that the asymptotic expansion yields the exact result after a finite number of terms. In each of these cases we derive a formula that bounds the order at which the expansion terminates. The method of calculation developed in this paper is applicable to similar families of integrals that involve Bessel or modified Bessel functions.