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Manuscript Title: A code to evaluate modified Bessel functions based on the continued fraction method.
Authors: J. Segura, P. Fernandez de Cordoba, Yu.L. Ratis
Program title: BESSIMIN, BESSIMSE
Catalogue identifier: ADGM_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 105(1997)263
Programming language: Fortran.
Computer: VAX 6410.
Operating system: VAX/VMS, UNIX.
Word size: 32
Keywords: General purpose, Modified, Bessel functions, Continued fraction, Method.
Classification: 4.7.

Nature of problem:
We include two codes in order to evaluate: (1) Modified Spherical Bessel function (subroutine BESSIMSE) (2) Modified Bessel functions of integral order (subroutine BESSIMIN). Both codes evaluate Modified Bessel functions from the lower (positive) orders to a maximum order NMAX in the same run.

Solution method:
We have developed a fast code to calculate modified Bessel functions of integral and half-integral order based on continued fractions. This algorithm is specially useful in the case of Bessel functions of high order because it does not require any recalculation using normalization relations.

Restrictions:
The maximum order that can be reached with our method, for a fixed real positive value of x, is provided by the maximum real number defined in our machine. The maximum x is limited by the same kind of restriction; however the overflow problem for high x can be eliminated by factoring out e**x for the K's and e**-x for the I's (see text (LONG WRITE-UP: section 5)).

Running time:
See text (LONG WRITE-UP: section 5)