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PreprintCC BY 4.0arXiv

Discrete orthogonal polynomials related to Hahn difference operator

  • J. F. Mañas-Mañas
  • J. J. Moreno-Balcázar
  • M. N. Rebocho
  • C. Rodr\'ıguez-Perales
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Abstract

This work studies general sequences of discrete orthogonal polynomials on linear lattices, including the so-called discrete Laguerre--Hahn orthogonal polynomials. We deduce the structure relations involving the orthogonal polynomials and their associated, as well as the explicit form of the fourth--order linear difference equation satisfied by these Laguerre--Hahn orthogonal polynomials. Furthermore, the particular cases corresponding to semiclassical and classical families of orthogonal polynomials, which lead to second--order difference equations, are also analyzed. Several examples illustrating the computation of the explicit coefficients of these difference equations for various families of orthogonal polynomials are also presented.

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Cite

BibTeXRIS
BibTeX
@misc{manasmanas2026discrete,
  title = {{Discrete orthogonal polynomials related to Hahn difference operator}},
  author = {J. F. Mañas-Mañas and J. J. Moreno-Balcázar and M. N. Rebocho and C. Rodr\'ıguez-Perales},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.30933},
  eprint = {2609.30933},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.30933},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Discrete orthogonal polynomials related to Hahn difference operator
AU  - J. F. Mañas-Mañas
AU  - J. J. Moreno-Balcázar
AU  - M. N. Rebocho
AU  - C. Rodr\'ıguez-Perales
PY  - 2026
DA  - 2026/09/25
PB  - arXiv
DO  - 10.48550/arxiv.2609.30933
UR  - https://arxiv.org/abs/2609.30933
AB  - This work studies general sequences of discrete orthogonal polynomials on linear lattices, including the so-called discrete Laguerre--Hahn orthogonal polynomials. We deduce the structure relations involving the orthogonal polynomials and their associated, as well as the explicit form of the fourth--order linear difference equation satisfied by these Laguerre--Hahn orthogonal polynomials. Furthermore, the particular cases corresponding to semiclassical and classical families of orthogonal polynomials, which lead to second--order difference equations, are also analyzed. Several examples illustrating the computation of the explicit coefficients of these difference equations for various families of orthogonal polynomials are also presented.
ER  -