2011-04-01
Algorithm 914: Parabolic Cylinder Function $W(a,x)$ and its Derivative
Publication
Publication
A Fortran 90 program for the computation of the real parabolic cylinder functions $W(a,\pm x),\,\,x\ge 0$ and their derivatives is presented. The code also computes scaled functions for $a>50$. The functions $W(a,\pm x)$ are a numerically satisfactory pair of solutions of the parabolic cylinder equation $y'' + \left(x^2/4 -a\right)y=0\,,\quad x\ge 0$. Using Wronskian tests, we claim a relative accuracy better than $5\,10^{-13}$ in the computable range of unscaled functions, while for scaled functions the aimed relative accuracy is better than $5\,10^{-14}$. This code, together with the algorithm and related software described in [Gil et al. 2006a],[Gil et al. 2006b] completes the set of software for parabolic cylinder functions (PCFs) for real arguments.
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Keywords | Parabolic cylinder functions, computation of special functions, ordinary differential equation integration, asymptotic expansions |
MSC | Confluent hypergeometric functions, Whittaker functions, ${}_1F_1$ (msc 33C15) |
Publisher | A.C.M. |
Journal | ACM Transactions on Mathematical Software |
Citation |
Gil, A, Segura, J, & Temme, N.M. (2011). Algorithm 914: Parabolic Cylinder Function $W(a,x)$ and its Derivative. ACM Transactions on Mathematical Software, 38(1).
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