McMahon-type asymptotic expansions of the zeros of the Coulomb wave functions
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929454853390336 |
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| author | Gil, Amparo Segura, Javier Temme, Nico M. |
| author_facet | Gil, Amparo Segura, Javier Temme, Nico M. |
| contents | We derive asymptotic expansions of the large zeros of the Coulomb wave functions and for those of their derivatives. The new expansions have the same form as the McMahon expansions of the zeros of the Bessel functions and reduce to them when a parameter is equal to zero. Numerical tests are provided to demonstrate the accuracy of the expansions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_14537 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | McMahon-type asymptotic expansions of the zeros of the Coulomb wave functions Gil, Amparo Segura, Javier Temme, Nico M. Classical Analysis and ODEs 33C47, 33C10, 33C15, 41A60, 65D20, 65H05 We derive asymptotic expansions of the large zeros of the Coulomb wave functions and for those of their derivatives. The new expansions have the same form as the McMahon expansions of the zeros of the Bessel functions and reduce to them when a parameter is equal to zero. Numerical tests are provided to demonstrate the accuracy of the expansions. |
| title | McMahon-type asymptotic expansions of the zeros of the Coulomb wave functions |
| topic | Classical Analysis and ODEs 33C47, 33C10, 33C15, 41A60, 65D20, 65H05 |
| url | https://arxiv.org/abs/2402.14537 |