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q-Differential equations for q-classical polynomials and q-Jacobi-Stirling numbers

Loureiro, Ana F., Zeng, J. (2016) q-Differential equations for q-classical polynomials and q-Jacobi-Stirling numbers. q-Differential equations for q-classical polynomials and q-Jacobi-Stirling numbers, 289 (5-6). pp. 693-717. (doi:10.1002/mana.201400381)

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Abstract

We introduce, characterise and provide a combinatorial interpretation for the so-called q-Jacobi–Stirling numbers. This study is motivated by their key role in the (reciprocal) expansion of any power of a second order q-differential operator having the q-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 q-version of those given by Everitt et al. and by the first author, whilst the combinatorics of this new set of numbers is a q-version of the Jacobi–Stirling numbers given by Gelineau and the second author.

Item Type: Article
DOI/Identification number: 10.1002/mana.201400381
Subjects: Q Science > QA Mathematics (inc Computing science)
Q Science > QA Mathematics (inc Computing science) > QA165 Combinatorics
Q Science > QA Mathematics (inc Computing science) > QA299 Analysis, Calculus
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Applied Mathematics
Depositing User: Ana F. Loureiro
Date Deposited: 29 May 2014 15:59 UTC
Last Modified: 29 May 2019 12:37 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/41224 (The current URI for this page, for reference purposes)
Loureiro, Ana F.: https://orcid.org/0000-0002-4137-8822
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