{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:10:13Z","timestamp":1760235013309,"version":"build-2065373602"},"reference-count":33,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2021,7,7]],"date-time":"2021-07-07T00:00:00Z","timestamp":1625616000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Andrews gave a remarkable interpretation of the Rogers\u2013Ramanujan identities with the polynomials \u03c1e(N,y,x,q), and it was noted that \u03c1e(\u221e,\u22121,1,q) is the generation of the fifth-order mock theta functions. In the present investigation, several interesting types of generating functions for this q-polynomial using q-difference equations is deduced. Besides that, a generalization of Andrew\u2019s result in form of a multilinear generating function for q-polynomials is also given. Moreover, we build a transformation identity involving the q-polynomials and Bailey transformation. As an application, we give some new Hecke-type identities. We observe that most of the parameters involved in our results are symmetric to each other. Our results are shown to be connected with several earlier works related to the field of our present investigation.<\/jats:p>","DOI":"10.3390\/sym13071222","type":"journal-article","created":{"date-parts":[[2021,7,8]],"date-time":"2021-07-08T04:32:49Z","timestamp":1625718769000},"page":"1222","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Applications of Generalized q-Difference Equations for General q-Polynomials"],"prefix":"10.3390","volume":"13","author":[{"given":"Zeya","family":"Jia","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Huanghuai University, Zhumadian 463000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2427-2003","authenticated-orcid":false,"given":"Bilal","family":"Khan","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences and Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai 200241, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qiuxia","family":"Hu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Luoyang Normal University, Luoyang 471934, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dawei","family":"Niu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Henan University of Animal Husbandry and Economy, Zhengzhou 450000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,7,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1134\/S0081543812010038","article-title":"q-Orthogonal polynomials, Rogers-Ramanujan identities and mock theta function","volume":"276","author":"Andrews","year":"2012","journal-title":"Proc. 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