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Manuscript Title: Airy function with complex arguments.
Authors: W. Moon
Program title: AIRY
Catalogue identifier: ABVX_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 22(1981)411
Programming language: Fortran.
Computer: AMDAHL V7.
Operating system: OS.
RAM: 18K words
Word size: 8
Keywords: Airy, Function, General purpose.
Classification: 4.7.

Nature of problem:
In theoretical seismology and electromagnetic theory, the Airy function often appears as a part of solutions and its usefulness can never be exaggerated in applied mathematics in general. This subroutine is written with particular applications in mind to be used in problems where the arguments become complex quantities.

Solution method:
For |z| < 3.5, the ascending series formulae are used and for |z| greater than 3.5, the asympotic formulae. These formulae are given by Abramowitz and Stegun. The critical number 3.5 is set arbitrarily in this case, and it can be changed to a more appropriate number as may be necessary. The accuracy of the Airy functions Ai(z), Bi(z) and their derivatives is set by the remainder term of the Ai(z) series which is set to be less than 1.0D-6. If this is found to be inappropriate for Bi(z) or the derivatives the error criteria can be changed easily in the program. However, the accuracy of the solution will not improve in the vicinity of |z| = 3.5, due to the inherent nature of the asymptotic series and ascending series.

There are no restrictions as long as the formulae are valid.

Running time:
2.71 s CPU.