Numerical and asymptotic aspects of parabolic cylinder functions
Journal of Computational and Applied Mathematics - Special issue on numerical analysis in the 20th century vol. 1: approximation theory
Algorithm 819: AIZ, BIZ: two Fortran 77 routines for the computation of complex Airy functions
ACM Transactions on Mathematical Software (TOMS)
Portable Special Function Routines
Portability of Numerical Software, Workshop
Integral representations for computing real parabolic cylinder functions
Numerische Mathematik
ACM Transactions on Mathematical Software (TOMS)
ACM Transactions on Mathematical Software (TOMS)
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Algorithm 850: Real parabolic cylinder functions U(a, x), V(a, x)
ACM Transactions on Mathematical Software (TOMS)
Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations
ACM Transactions on Mathematical Software (TOMS)
Algorithm 914: Parabolic cylinder function W(a, x) and its derivative
ACM Transactions on Mathematical Software (TOMS)
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Methods for the computation of real parabolic cylinder functions U(a, x), and V(a, x) and their derivatives are described. We give details on power series, asymptotic series, recursion and quadrature. A combination of these methods can be used for computing parabolic cylinder functions for unrestricted values of the order a and the variable x except for the overflow/underflow limitations. By factoring the dominant exponential factor, scaled functions can be computed without practical overflow/underflow limitations. In an accompanying article we describe the precise domains for these methods and we present the Fortran 90 codes for the computation of these functions.