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arXiv · 2210.16982

Computation of parabolic cylinder functions having complex argument

T. M. Dunster·A. Gil·J. Segura
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Abstract

Numerical methods for the computation of the parabolic cylinder $U(a,z)$ for real $a$ and complex $z$ are presented. The main tools are recent asymptotic expansions involving exponential and Airy functions, with slowly varying analytic coefficient functions involving simple coefficients, and stable integral representations; these two main main methods can be complemented with Maclaurin series and a Poincar\'e asymptotic expansion. We provide numerical evidence showing that the combination of these methods is enough for computing the function with $5\times 10^{-13}$ relative accuracy in double precision floating point arithmetic.

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T. M. Dunster, A. Gil, J. Segura. 2022-10-30. Computation of parabolic cylinder functions having complex argument. https://arxiv.org/abs/2210.16982

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