NUMERICAL EVALUATION OF AIRY FUNCTIONS WITH COMPLEX ARGUMENTS

We present two methods for the evaluation of Airy functions of complex argument. The first method is accurate to any desired precision but is slow and unsuitable for fixed-precision languages. The second method is accurate to double precision (12 digits) and is suitable for programming in a fixed-precision language such as FORTRAN. The first method uses the symbolic manipulation language Maple to evaluate either the Taylor series expansion or an asymptotic expansion of each function. The second method extends an idea of J. C. P. Miller to the complex plane. It uses the first method to obtain a grid of points in the complex plane where the functions are known to high precision and then uses Taylor series from these base points. The resulting algorithm is accurate and efficient. © 1992.