Multiple orthogonal polynomials, $d$-orthogonal polynomials, production matrices, and branched continued fractions
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2022
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866910515331072000 |
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| author | Sokal, Alan D. |
| author_facet | Sokal, Alan D. |
| contents | I analyze an unexpected connection between multiple orthogonal polynomials, $d$-orthogonal polynomials, production matrices and branched continued fractions. This work can be viewed as a partial extension of Viennot's combinatorial theory of orthogonal polynomials to the case where the production matrix is lower-Hessenberg but is not necessarily tridiagonal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_11528 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Multiple orthogonal polynomials, $d$-orthogonal polynomials, production matrices, and branched continued fractions Sokal, Alan D. Classical Analysis and ODEs Combinatorics 42C05 (Primary), 05A15, 05A19, 15A24, 15A99, 15B99, 30B70, 30E05, 33C45, 41A21 (Secondary) I analyze an unexpected connection between multiple orthogonal polynomials, $d$-orthogonal polynomials, production matrices and branched continued fractions. This work can be viewed as a partial extension of Viennot's combinatorial theory of orthogonal polynomials to the case where the production matrix is lower-Hessenberg but is not necessarily tridiagonal. |
| title | Multiple orthogonal polynomials, $d$-orthogonal polynomials, production matrices, and branched continued fractions |
| topic | Classical Analysis and ODEs Combinatorics 42C05 (Primary), 05A15, 05A19, 15A24, 15A99, 15B99, 30B70, 30E05, 33C45, 41A21 (Secondary) |
| url | https://arxiv.org/abs/2204.11528 |