q-Differential equations for q-classical polynomials and q-Jacobi-Stirling numbers
Classical Analysis and ODEs
2015-07-07 v2 Combinatorics
Abstract
We introduce, characterise and provide a combinatorial interpretation for the so-called -Jacobi-Stirling numbers. This study is motivated by their key role in the (reciprocal) expansion of any power of a second order -differential operator having the -classical polynomials as eigenfunctions in terms of other even order operators, which we explicitly construct in this work. The results here obtained can be viewed as the -version of those given by Everitt {\it et al.} and by the first author, whilst the combinatorics of this new set of numbers is a -version of the Jacobi-Stirling numbers given by Gelineau and the second author.
Keywords
Cite
@article{arxiv.1309.4968,
title = {q-Differential equations for q-classical polynomials and q-Jacobi-Stirling numbers},
author = {Ana F. Loureiro and Jiang Zeng},
journal= {arXiv preprint arXiv:1309.4968},
year = {2015}
}
Comments
version accepted for publication in Mathematische Nachrichten