Uniform asymptotic expansions for the zeros of parabolic cylinder functions
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916342080208896 |
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| author | Dunster, T. M. Gil, A. Ruiz-Antolin, D. Segura, J. |
| author_facet | Dunster, T. M. Gil, A. Ruiz-Antolin, D. Segura, J. |
| contents | The real and complex zeros of the parabolic cylinder function $U(a,z)$ are studied. Asymptotic expansions for the zeros are derived, involving the zeros of Airy functions, and these are valid for $a$ positive or negative and large in absolute value, uniformly for unbounded $z$ (real or complex). The accuracy of the approximations of the complex zeros is then demonstrated with some comparative tests using a highly precise numerical algorithm for finding the complex zeros of the function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_13936 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Uniform asymptotic expansions for the zeros of parabolic cylinder functions Dunster, T. M. Gil, A. Ruiz-Antolin, D. Segura, J. Classical Analysis and ODEs 33C15, 33C45, 34E20, 34C10, 33F05 The real and complex zeros of the parabolic cylinder function $U(a,z)$ are studied. Asymptotic expansions for the zeros are derived, involving the zeros of Airy functions, and these are valid for $a$ positive or negative and large in absolute value, uniformly for unbounded $z$ (real or complex). The accuracy of the approximations of the complex zeros is then demonstrated with some comparative tests using a highly precise numerical algorithm for finding the complex zeros of the function. |
| title | Uniform asymptotic expansions for the zeros of parabolic cylinder functions |
| topic | Classical Analysis and ODEs 33C15, 33C45, 34E20, 34C10, 33F05 |
| url | https://arxiv.org/abs/2407.13936 |