On Temme's Algorithm for the Modified Bessel Function of the Third Kind
- 1 December 1980
- journal article
- Published by Association for Computing Machinery (ACM) in ACM Transactions on Mathematical Software
- Vol. 6 (4) , 581-586
- https://doi.org/10.1145/355921.355928
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 --- ½ 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 L÷dx) and the Wronskian to obtam K,.(x) and K,+dx)Keywords
This publication has 5 references indexed in Scilit:
- Bessel functions Jv(x) and Yv(x) of real order and real argumentComputer Physics Communications, 1979
- New backward recurrences for Bessel functionsMathematics of Computation, 1979
- On the numerical evaluation of the modified bessel function of the third kindJournal of Computational Physics, 1975
- Computational Aspects of Three-Term Recurrence RelationsSIAM Review, 1967
- Numerical Evaluation of Continued FractionsSIAM Review, 1964