On Second Order q-Difference Equations Satisfied by Al-Salam–Carlitz I-Sobolev Type Polynomials of Higher Order
This contribution deals with the sequence {U (a) n (x; q, j)}n≥0 of monic polynomials in x, orthogonal with respect to a Sobolev-type inner product related to the Al-Salam–Carlitz I orthogonal polynomials, and involving an arbitrary number j of q-derivatives on the two boundaries of the correspondin...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2020 |
| País: | España |
| Institución: | Universidad Loyola Andalucía |
| Repositorio: | Brújula |
| OAI Identifier: | oai:repositorio.uloyola.es:20.500.12412/6375 |
| Acceso en línea: | https://hdl.handle.net/20.500.12412/6375 https://doi.org/10.3390/math8081300 |
| Access Level: | acceso abierto |
| Palabra clave: | Al-Salam–Carlitz I polynomials Al-Salam–Carlitz I-Sobolev type polynomials Second order linear q-difference equations Structure relations Recurrence relations Basic hypergeometric series |
| Sumario: | This contribution deals with the sequence {U (a) n (x; q, j)}n≥0 of monic polynomials in x, orthogonal with respect to a Sobolev-type inner product related to the Al-Salam–Carlitz I orthogonal polynomials, and involving an arbitrary number j of q-derivatives on the two boundaries of the corresponding orthogonality interval, for some fixed real number q ∈ (0, 1). We provide several versions of the corresponding connection formulas, ladder operators, and several versions of the second order q-difference equations satisfied by polynomials in this sequence. As a novel contribution to the literature, we provide certain three term recurrence formula with rational coefficients satisfied by U (a) n (x; q, j), which paves the way to establish an appealing generalization of the so-called J-fractions to the framework of Sobolev-type orthogonality |
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