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This study is motivated by their key role in the (reciprocal) expansion of any power of a second order <jats:italic>q<\/jats:italic>\u2010differential operator having the <jats:italic>q<\/jats:italic>\u2010classical 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 <jats:italic>q<\/jats:italic>\u2010version of those given by Everitt et\u00a0al. and by the first author, whilst the combinatorics of this new set of numbers is a <jats:italic>q<\/jats:italic>\u2010version of the Jacobi\u2013Stirling numbers given by Gelineau and the second author.<\/jats:p>","DOI":"10.1002\/mana.201400381","type":"journal-article","created":{"date-parts":[[2015,10,7]],"date-time":"2015-10-07T16:11:22Z","timestamp":1444234282000},"page":"693-717","source":"Crossref","is-referenced-by-count":1,"title":["\u2010differential equations for \u2010classical polynomials and \u2010Jacobi\u2013Stirling numbers"],"prefix":"10.1002","volume":"289","author":[{"given":"Ana F.","family":"Loureiro","sequence":"first","affiliation":[{"name":"School of Mathematics, Statistics &amp; Actuarial Science (SMSAS), Cornwallis Building University of Kent Canterbury Kent CT2 7NF U.K."}]},{"given":"Jiang","family":"Zeng","sequence":"additional","affiliation":[{"name":"Universit\u00e9 de Lyon, Universit\u00e9 Claude Bernard Lyon\u00a01 Institut Camille Jordan UMR 5208 du CNRS, 43 boulevard du 11 novembre 1918 69622 Villeurbanne cedex France"}]}],"member":"311","published-online":{"date-parts":[[2015,10,7]]},"reference":[{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-0427(00)00585-9"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcta.2012.08.006"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01180560"},{"key":"e_1_2_1_5_1","volume-title":"An Introduction to Orthogonal Polynomials","author":"Chihara T. 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