Integral Representations for Computing Real Parabolic Cylinder Functions
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2004
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| _version_ | 1866917022822039552 |
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| author | Gil, Amparo Segura, Javier Temme, Nico M. |
| author_facet | Gil, Amparo Segura, Javier Temme, Nico M. |
| contents | Integral representations are derived for the parabolic cylinder functions $U(a,x)$, $V(a,x)$ and $W(a,x)$ and their derivatives. The new integrals will be used in numerical algorithms based on quadrature. They follow from contour integrals in the complex plane, by using methods from asymptotic analysis (saddle point and steepest descent methods), and are stable starting points for evaluating the functions $U(a,x)$, $V(a,x)$ and $W(a,x)$ and their derivatives by quadrature rules. In particular, the new representations can be used for large parameter cases. Relations of the integral representations with uniform asymptotic expansions are also given. The algorithms will be given in a future paper. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_math_0401131 |
| institution | arXiv |
| publishDate | 2004 |
| record_format | arxiv |
| spellingShingle | Integral Representations for Computing Real Parabolic Cylinder Functions Gil, Amparo Segura, Javier Temme, Nico M. Numerical Analysis Classical Analysis and ODEs 33C15, 41A60, 65D20 Integral representations are derived for the parabolic cylinder functions $U(a,x)$, $V(a,x)$ and $W(a,x)$ and their derivatives. The new integrals will be used in numerical algorithms based on quadrature. They follow from contour integrals in the complex plane, by using methods from asymptotic analysis (saddle point and steepest descent methods), and are stable starting points for evaluating the functions $U(a,x)$, $V(a,x)$ and $W(a,x)$ and their derivatives by quadrature rules. In particular, the new representations can be used for large parameter cases. Relations of the integral representations with uniform asymptotic expansions are also given. The algorithms will be given in a future paper. |
| title | Integral Representations for Computing Real Parabolic Cylinder Functions |
| topic | Numerical Analysis Classical Analysis and ODEs 33C15, 41A60, 65D20 |
| url | https://arxiv.org/abs/math/0401131 |