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Algorithm 831: Modified Bessel functions of imaginary order and positive argument

Algorithm 831: Modified Bessel functions of imaginary order and positive argument Fortran 77 programs for the computation of modified Bessel functions of purely imaginary order are presented. The codes compute the functions K ia ( x ), L ia ( x ) and their derivatives for real a and positive x ; these functions are independent solutions of the differential equation x 2 w" + xw ' + ( a 2 − x 2 ) w = 0. The code also computes exponentially scaled functions. The range of computation is ( x , a ) ∈ (0,1500 × −1500, 1500 when scaled functions are considered and it is larger than (0,500 × −400, 400 for standard IEEE double precision arithmetic. The relative accuracy is better than 10 −13 in the range (0,200 × −200, 200 and close to 10 −12 in (0, 1500 × −1500, 1500. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Mathematical Software (TOMS) Association for Computing Machinery

Algorithm 831: Modified Bessel functions of imaginary order and positive argument

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Publisher
Association for Computing Machinery
Copyright
Copyright © 2004 by ACM Inc.
ISSN
0098-3500
DOI
10.1145/992200.992204
Publisher site
See Article on Publisher Site

Abstract

Fortran 77 programs for the computation of modified Bessel functions of purely imaginary order are presented. The codes compute the functions K ia ( x ), L ia ( x ) and their derivatives for real a and positive x ; these functions are independent solutions of the differential equation x 2 w" + xw ' + ( a 2 − x 2 ) w = 0. The code also computes exponentially scaled functions. The range of computation is ( x , a ) ∈ (0,1500 × −1500, 1500 when scaled functions are considered and it is larger than (0,500 × −400, 400 for standard IEEE double precision arithmetic. The relative accuracy is better than 10 −13 in the range (0,200 × −200, 200 and close to 10 −12 in (0, 1500 × −1500, 1500.

Journal

ACM Transactions on Mathematical Software (TOMS)Association for Computing Machinery

Published: Jun 1, 2004

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