# 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 10.1002/mana.201400381 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 Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Applied Mathematics Ana F. Loureiro 29 May 2014 15:59 UTC 29 May 2019 12:37 UTC https://kar.kent.ac.uk/id/eprint/41224 (The current URI for this page, for reference purposes) https://orcid.org/0000-0002-4137-8822
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