On Temme's Algorithm for the Modified Bessel Function of the Third Kind

Abstract

Some modlficatmns to Temme's algorithm for the evaluation of the modified Bessel functmn of the third kind have been made Temme evaluates K,(x) and K,+dx) for x > 1 and ]~1 --- from auxdmry functmns k(,(x) and kdx), which he determines by Miller's backward recurrence algorithm In this paper the starting order for the backward recurrence algorithm for ko(x) and k~(x) is given by a pmcewlse linear functmn of 1/x Also, we have found that ~t is more efficmnt, for small values of x, to calculate only kdx)/ko(x), whmh can be used with the values L(x) and Ldx) and the Wronskian to obtam K,.(x) and K,+dx)