Computation of Modified Bessel Functions and Their Ratios

Abstract

An efficient algorithm for calculating ratios rnu(x) = Inu+1(x)/Inu(x), nu geqq 0, x geqq 0, is presented. This algorithm in conjunction with the recursion relation for rnu(x) gives an alternative to other recursive methods for Inu(x) when approximations for low-order Bessel functions are available. Sharp bounds on rnu(x) and Inu(x) are also established in addition to some monotonicity properties of rnu(x) and rnu'(x).