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Manuscript Title: Bessel functions Inu(z) and Knu(z) of real order and complex argument.
Authors: J.B. Campbell
Program title: BESSIK
Catalogue identifier: AAQZ_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 24(1981)97
Programming language: Fortran.
Computer: IBM 3033.
Operating system: TSS/370.
RAM: 15K words
Word size: 32
Keywords: General purpose, Bessel, Cylindrical, Backward recurrence, Miller's algorithm, Complex functions.
Classification: 4.7.

Revision history:
Type Tit le Reference
correction 000A CORRECTION 28/10/81 See below

Nature of problem:
Bessel functions appear in a large number of physical problems, e.g. the solution of potential problems in cylindrical coordinates.

Solution method:
For arguments of small or moderately large modulus, Iv(z) is computed by Miller's backward recurrence algorithm described by Gautschi. For arguments of large modulus, Iv(z) is determined from its asymptotic expansion for large argument and backward recurrence. Kv(z) and Kv+1(z) for |v|<=1/2 are determined from Neumann series when real part of z is small and from Temme's algorithm and some modifications for arguments of moderately large or large modulus. For real arguments, Temme's algorithm for small arguments is also used. Kv(z) for large order is obtained from the forward recurrence.

Restrictions:
The functions are determined only for non-negative order. Kv(z) is determined only for values of z with non-negative real part. The subroutines are inefficient when both order and modulus of argument are very large.

Running time:
For order and modulus of argument not both large, the determination of a single function requires less than 1.6 ms. The determination of a sequence of functions with the orders of two successive members of the sequence differing by 1 requires, in addition, 15 ms for each member of the sequence. The running times of subroutines RBESI and RBESK for real argument are comparable to those of RBESJ and RBESY and are about 1/2 to 1/3 of the running times of subroutines CBESI and CBESK for complex argument. Running times on the IBM 3033 are about 1.9 times faster than times on the IBM 3032.

CORRECTION SUMMARY
Manuscript Title: Bessel functions Inu(z) and Knu(z) of real order and complex argument. (C.P.C. 24(1981)97).
Authors: J.B. Campbell
Program title: 000A CORRECTION 28/10/81
Catalogue identifier: AAQZ_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 25(1982)207
Classification: 4.7.