  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.
