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A Recursive Method for Computing Certain Bessel Function Integrals

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.