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