On Polynomials Orthogonal with Respect to an Inner Product Involving Higher-Order Differences: The Meixner Case
In this contribution we consider sequences of monic polynomials orthogonal with respect to the Sobolev-type inner product h f , gi = huM , f gi + λT j f (α)T j g(α), where uM is the Meixner linear operator, λ ∈ R+ , j ∈ N, α ≤ 0, and T is the forward difference operator ∆ or the backward difference...
| Autores: | , , |
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| Formato: | artículo |
| Fecha de publicación: | 2022 |
| País: | España |
| Recursos: | Universidad Loyola Andalucía |
| Repositorio: | Brújula |
| OAI Identifier: | oai:repositorio.uloyola.es:20.500.12412/6379 |
| Acesso em linha: | https://hdl.handle.net/20.500.12412/6379 |
| Access Level: | acceso abierto |
| Palavra-chave: | Meixner polynomials Meixner–Sobolev orthogonal polynomials Discrete kernel polynomials |
| Resumo: | In this contribution we consider sequences of monic polynomials orthogonal with respect to the Sobolev-type inner product h f , gi = huM , f gi + λT j f (α)T j g(α), where uM is the Meixner linear operator, λ ∈ R+ , j ∈ N, α ≤ 0, and T is the forward difference operator ∆ or the backward difference operator ∇. Moreover, we derive an explicit representation for these polynomials. The ladder operators associated with these polynomials are obtained, and the linear difference equation of the second order is also given. In addition, for these polynomials, we derive a (2j + 3)-term recurrence relation. Finally, we find the Mehler–Heine type formula for the particular case α = 0. |
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