Artículo
Structural Formulas for Matrix-Valued Orthogonal Polynomials Related to 2×2 Hypergeometric Operators
Autor/es | Calderón, C.
Castro Smirnova, Mirta María |
Departamento | Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI) |
Fecha de publicación | 2022-03 |
Fecha de depósito | 2023-01-19 |
Publicado en |
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Resumen | We give some structural formulas for the family of matrix-valued orthogonal polynomials of size 2×2
introduced by C. Calderón et al. in an earlier work, which are common eigenfunctions of a differential operator of ... We give some structural formulas for the family of matrix-valued orthogonal polynomials of size 2×2 introduced by C. Calderón et al. in an earlier work, which are common eigenfunctions of a differential operator of hypergeometric type. Specifically, we give a Rodrigues formula that allows us to write this family of polynomials explicitly in terms of the classical Jacobi polynomials, and write, for the sequence of orthonormal polynomials, the three-term recurrence relation and the Christoffel–Darboux identity. We obtain a Pearson equation, which enables us to prove that the sequence of derivatives of the orthogonal polynomials is also orthogonal, and to compute a Rodrigues formula for these polynomials as well as a matrix-valued differential operator having these polynomials as eigenfunctions. We also describe the second-order differential operators of the algebra associated with the weight matrix. |
Agencias financiadoras | FEDER (EU) / Ministerio de Ciencia e Innovación-Agencia Estatal de Investigación PGC2018-096504-B-C31 Junta de Andalucía and FEDER (EU) US-1254600 |
Identificador del proyecto | PGC2018-096504-B-C31
US-1254600 |
Cita | Calderón, C. y Castro Smirnova, M.M. (2022). Structural Formulas for Matrix-Valued Orthogonal Polynomials Related to 2×2 Hypergeometric Operators. Bulletin of the Malaysian Mathematical Sciences Society, 45, 697-726. https://doi.org/10.1007/s40840-021-01211-x. |
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