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Zbl 1074.33017
Fabijonas, B.R.; Lozier, D.W.; Olver, F.W.J.
Computation of complex Airy functions and their zeros using asymptotics and the differential equation. (English)
[J] ACM Trans. Math. Softw. 30, No. 4, 471-490 (2004). ISSN 0098-3500

Summary: We describe a method by which one can compute the solutions of Airy's differential equation, and their derivatives, both on the real line and in the complex plane. The computational methods are numerical integration of the differential equation and summation of asymptotic expansions for large argument. We give details involved in obtaining all of the parameter values, and we control the truncation errors rigorously. Using the same computational methods, we describe an algorithm that computes the zeros and associated values of the Airy functions and their derivatives, and the modulus and phase functions on the negative real axis.

MSC 2000:: *33F05 Numerical approximation of special functions
65D20 Computation of special functions

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