English

Hahn multiple orthogonal polynomials of type I: Hypergeometrical expressions

Classical Analysis and ODEs 2023-01-02 v2 Mathematical Physics math.MP

Abstract

Explicit expressions for the Hahn multiple polynomials of type I, in terms of Kamp\'e de F\'eriet hypergeometric series, are given. Orthogonal and biorthogonal relations are proven. Then, part of the Askey scheme for multiple orthogonal polynomials type I is completed. In particular, explicit expressions in terms of generalized hypergeometric series and Kamp\'e de F\'eriet hypergeometric series, are given for the multiple orthogonal polynomials of type I for the Jacobi-Pi\~neiro, Meixner I, Meixner II, Kravchuk, Laguerre I, Laguerre II and Charlier families.

Keywords

Cite

@article{arxiv.2212.11923,
  title  = {Hahn multiple orthogonal polynomials of type I: Hypergeometrical expressions},
  author = {Amílcar Branquinho and Juan E. F. Díaz and Ana Foulquié-Moreno and Manuel Mañas},
  journal= {arXiv preprint arXiv:2212.11923},
  year   = {2023}
}

Comments

27 pages. Minor typos corrected

R2 v1 2026-06-28T07:49:25.513Z