Uniform asymptotic expansions for the zeros of parabolic cylinder functions
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 accu...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universidad de Cantabria (UC) |
| Repositorio: | UCrea Repositorio Abierto de la Universidad de Cantabria |
| Idioma: | inglés |
| OAI Identifier: | oai:repositorio.unican.es:10902/35871 |
| Acceso en línea: | https://hdl.handle.net/10902/35871 |
| Access Level: | acceso abierto |
| Palabra clave: | Parabolic cylinder functions Hermite polynomials Zeros Turning point theory |
| Sumario: | 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. |
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