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Zbl 1001.65021
Segura, J.; Gil, A.
Parabolic cylinder functions of integer and half-integer orders for nonnegative arguments. (English)
[J] Comput. Phys. Commun. 115, No.1, 69-86 (1998). ISSN 0010-4655

Summary: We present two codes to evaluate parabolic cylinder functions $\{V(a,x),U(a,x)\}$ for integer and half-integer positive values of $a$ and for nonnegative $x$. The codes are based on the forward application of the recurrence relation for $V(a,x)$, the backward recurrence for $U(a,x)$, the Wronskian relation between $V(a,x)$ and $U(a,x)$, and the evaluation of a continued fraction for the ratio $U(a,x)/U(a-1,x)$. The accuracy obtained is better than $10^{-12}$ for $0<x<1.0$ and better than $10^{-14}$ for $x>1$. We discuss some applications of the codes.

MSC 2000:: *65D20 Computation of special functions
33C10 Cylinder functions, etc.
33F05 Numerical approximation of special functions

Keywords: three term recurrence relations; parabolic cylinder functions; continued fraction

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