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Zbl 0777.65007
Nardin, Mark; Perger, W.F.; Bhalla, Atul
Numerical evaluation of the confluent hypergeometric function for complex arguments of large magnitudes. (English)
[J] J. Comput. Appl. Math. 39, No.2, 193-200 (1992). ISSN 0377-0427

The authors describe a numerical evaluator for the confluent hypergeometric function for complex arguments with large magnitudes using a direct summation of Kummer's series. Extended precision subroutines using large integer arrays to accumulate a single numerator and denominator are ultimately used in a single division to arrive at the final result. The accuracy has been verified through a variety of tests and they show the evaluator to be consistently accurate to thirteen significant figures, and on rare occasion accurate to only nine for magnitudes of the arguments ranging into the thousands in any quadrant in the complex plane.
[J.Prakash (Bombay)]

MSC 2000:: *65D20 Computation of special functions
65E05 Numerical methods in complex analysis
33C15 Confluent hypergeometric functions
30E10 Approximation in the complex domain

Keywords: confluent hypergeometric function; complex arguments; Kummer's series

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