2013/09/19 by Ana F. Loureiro, Jiang Zeng, Loureiro, Ana F. +1
Mathematics · #Advanced Combinatorial Mathematics #Mathematical functions and polynomials #Advanced Mathematical Identities
paper · pdf · doi:10.48550/arxiv.1309.4968
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 \it 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.