Orthogonal Polynomials with a Singularly Perturbed Airy Weight
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910386756780032 |
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| author | Min, Chao Cheng, Yuan |
| author_facet | Min, Chao Cheng, Yuan |
| contents | We study the monic orthogonal polynomials with respect to a singularly perturbed Airy weight. By using Chen and Ismail's ladder operator approach, we derive a discrete system satisfied by the recurrence coefficients for the orthogonal polynomials. We find that the orthogonal polynomials satisfy a second-order linear ordinary differential equation, whose coefficients are all expressed in terms of the recurrence coefficients. By considering the time evolution, we obtain a system of differential-difference equations satisfied by the recurrence coefficients. Finally, we study the asymptotics of the recurrence coefficients when the degrees of the orthogonal polynomials tend to infinity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_18669 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Orthogonal Polynomials with a Singularly Perturbed Airy Weight Min, Chao Cheng, Yuan Classical Analysis and ODEs Mathematical Physics 33C45, 42C05 We study the monic orthogonal polynomials with respect to a singularly perturbed Airy weight. By using Chen and Ismail's ladder operator approach, we derive a discrete system satisfied by the recurrence coefficients for the orthogonal polynomials. We find that the orthogonal polynomials satisfy a second-order linear ordinary differential equation, whose coefficients are all expressed in terms of the recurrence coefficients. By considering the time evolution, we obtain a system of differential-difference equations satisfied by the recurrence coefficients. Finally, we study the asymptotics of the recurrence coefficients when the degrees of the orthogonal polynomials tend to infinity. |
| title | Orthogonal Polynomials with a Singularly Perturbed Airy Weight |
| topic | Classical Analysis and ODEs Mathematical Physics 33C45, 42C05 |
| url | https://arxiv.org/abs/2403.18669 |