ACM Transactions on Mathematical Software (TOMS)
Numerical evaluation of airy functions with complex arguments
Journal of Computational Physics
ACM Transactions on Mathematical Software (TOMS)
Algorithm 644: A portable package for Bessel functions of a complex argument and nonnegative order
ACM Transactions on Mathematical Software (TOMS)
Algorithm 498: Airy Functions Using Chebyshev Series Approximations
ACM Transactions on Mathematical Software (TOMS)
Remark on “Algorithm 498: Airy Functions Using Chebyshev Series Approximations”
ACM Transactions on Mathematical Software (TOMS)
Communications of the ACM
Asymptotic approximations of integrals
Asymptotic approximations of integrals
Algorithm 819: AIZ, BIZ: two Fortran 77 routines for the computation of complex Airy functions
ACM Transactions on Mathematical Software (TOMS)
Algorithms and codes for the Macdonald function: recent progress and comparisons
Journal of Computational and Applied Mathematics
ACM Transactions on Mathematical Software (TOMS)
ACM Transactions on Mathematical Software (TOMS)
Computing the real parabolic cylinder functions U(a, x), V(a, x)
ACM Transactions on Mathematical Software (TOMS)
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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.