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Manuscript Title: Modified Bessel functions Imu(z) and Kmu(z) of real order and complex argument, to selected accuracy.
Authors: I.J. Thompson, A.R. Barnett
Program title: BESSCC
Catalogue identifier: ABBM_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 47(1987)245
Programming language: Fortran.
Computer: NAS 7000, CRAY-1, ATLAS-10, IBM 3081, CYBER 205, GEC 4190, CDC 7600, IBM PC/AT, ZENITH 248, VAX 750.
Operating system: MVS.
RAM: 360K words
Word size: 64
Keywords: GENERAL PURPOSE, BESSEL, CONTINUED FRACTION, TEMME, CYLINDRICAL, MILLER'S ALGORITHM, STEED'S METHOD, BACKWARD RECURRENCE, AIRY, KELVIN, MODIFIED.
Classification: 4.7.

Revision history:
Type Tit le Reference
correction 000A CORRECTION 20/04/04 See below

Nature of problem:
The BESSCC subroutine calculates the modified Bessel functions Imu(z) and Kmu(z) (and derivatives) for complex argument z and a sequence of real orders mu,mu+1,...,mu+n-1 for integer N >/= 1. These functions arise in the solutions of potential problems in spherical and cylindrical coordinates. They can also be used to calculate ordinary Bessels Jmu(z), Ymu(z), spherical Bessels Jmu(z), Ymu(z), Kelvin and Airy functions.

Solution method:
For large arguments z, Temme's algorithm is used to find Kmu, Kmu' and Imu, Imu'. The Imu(z) values are recurred upward (if this is stable). For moderate z, Kmu and Kmu' are found using Temme's method, and Miller's method is used to find Imu'/Imu, with Imu normalised by the Wronskian with Kmu. For small z, Miller's method is again used for the Imu, and a Neumann series for the Kmu(z). Upward recurrence of the Kmu is always stable, and downward recurrence for the Imu is used in the second and third cases.

Restrictions:
The functions are determined only for real order mu > -1/2. Reflection formulae are given for mu <= -1/2, and for complex order mu the procedure COULCC of Comp. Phys. Commun. 36(1985)363 is available. The routines are less efficient when both order and argument are large, becoming noticeable when mu+N > |Z|/2 > 1000.

Running time:
The test deck takes 0.44 secs of execution time on a NAS 7000.

CORRECTION SUMMARY
Manuscript Title: Modified Bessel functions Imu(z) and Kmu(z) of real order and complex argument, to selected accuracy.
Authors: I.J. Thompson
Program title: 000A CORRECTION 20/04/04
Catalogue identifier: ABBM_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 159(2004)243
Classification: 4.7.