On the computation of certain integrals containing the modified Bessel function 𝐼₀(𝜉)

Abstract

Efficient stratagems are developed for numerically evaluating one- and two-dimensional integrals over x, y with integrand exp ⁡ ( − x − y ) I 0 ( 2 p x y ) \exp ( - x - y){I_0}(2\sqrt {pxy} ) . The integrals are expressed in terms of convergent series, which exhibit the correct limiting behavior, and which can be evaluated recursively. The performances of these stratagems are compared with numerical integration.