{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T07:40:01Z","timestamp":1760082001497,"version":"build-2065373602"},"reference-count":24,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2025,9,9]],"date-time":"2025-09-09T00:00:00Z","timestamp":1757376000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100009392","name":"Prince Sattam Bin Abdulaziz University","doi-asserted-by":"publisher","award":["PSAU\/2024\/01\/31729"],"award-info":[{"award-number":["PSAU\/2024\/01\/31729"]}],"id":[{"id":"10.13039\/100009392","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This study presents a novel variant of a finite q-Hankel transform derived from big q-Bessel functions and investigates its analytical structure, with particular emphasis on the distribution and properties of its zeros. A key focus is placed on the inherent symmetry in the zero distribution of these transforms, which plays a central role in their analytical characterization. We establish rigorous conditions under which the finite q-Hankel transforms exhibit only real zeros and demonstrate their adherence to well-defined asymptotic and symmetric patterns. Moreover, we introduce a series of q-analogs to classical theorems, such as those of P\u00f3lya, further illustrating the symmetric nature of these results within the framework of q-calculus. The findings not only deepen the understanding of q-integral transforms and their symmetry properties but also underscore their relevance in the broader context of special functions and mathematical analysis.<\/jats:p>","DOI":"10.3390\/sym17091498","type":"journal-article","created":{"date-parts":[[2025,9,9]],"date-time":"2025-09-09T19:16:17Z","timestamp":1757445377000},"page":"1498","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Advancements in q-Hankel Transforms Based on Certain Approach of Big q-Bessel Functions and Applications"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1687-3212","authenticated-orcid":false,"given":"Ola A.","family":"Ashour","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Science and Humanities, Prince Sattam bin Abdulaziz University, Al-Kharj 16278, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9027-0810","authenticated-orcid":false,"given":"Rajagopalan","family":"Ramaswamy","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science and Humanities, Prince Sattam bin Abdulaziz University, Al-Kharj 16278, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Karima M.","family":"Oraby","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science and Humanities, Prince Sattam bin Abdulaziz University, Al-Kharj 16278, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,9,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1112\/plms\/s2-2.1.192","article-title":"The applications of basic numbers to Bessel\u2019s and Legendre\u2019s equations","volume":"2","author":"Jackson","year":"1905","journal-title":"Proc. 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