{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,13]],"date-time":"2026-01-13T09:12:03Z","timestamp":1768295523346,"version":"3.49.0"},"reference-count":20,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,1,3]],"date-time":"2023-01-03T00:00:00Z","timestamp":1672704000000},"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>In this study, we introduce modified degenerate Changhee\u2013Genocchi polynomials of the second kind, and analyze some properties by providing several relations and applications. We first attain diverse relations and formulas covering addition formulas, recurrence rules, implicit summation formulas, and relations with the earlier polynomials in the literature. By using their generating function, we derive some new relations, including the Stirling numbers of the first and second kinds. Moreover, we introduce modified higher-order degenerate Changhee\u2013Genocchi polynomials of the second kind. We also derive some new identities and properties of this type of polynomials.<\/jats:p>","DOI":"10.3390\/sym15010136","type":"journal-article","created":{"date-parts":[[2023,1,3]],"date-time":"2023-01-03T02:33:21Z","timestamp":1672713201000},"page":"136","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A Note on Modified Degenerate Changhee\u2013Genocchi Polynomials of the Second Kind"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4681-9885","authenticated-orcid":false,"given":"Waseem Ahmad","family":"Khan","sequence":"first","affiliation":[{"name":"Department of Mathematics and Natural Sciences, Prince Mohammad Bin Fahd University, P.O. Box 1664, Al Khobar 31952, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5567-7444","authenticated-orcid":false,"given":"Maryam Salem","family":"Alatawi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Alatawi, M.S., and Khan, W.A. (2022). New type of degenerate Changhee-Genocchi polynomials. Axioms, 11.","DOI":"10.3390\/axioms11080355"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Khan, W.A., and Alatawi, M.S. (2022). Analytical properties of degenerate Genocchi polynomials the second kind and some of their applications. Symmetry, 14.","DOI":"10.3390\/sym14081500"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"428","DOI":"10.1186\/s13662-020-02891-8","article-title":"New type of degenerate Daehee polynomials of the second kind","volume":"2020","author":"Sharma","year":"2020","journal-title":"Adv. Differ. Equ."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Khan, W.A. (2022). A note on q-analogue of degenerate Catalan numbers associated with p-adic integral on Zp. Symmetry, 14.","DOI":"10.3390\/sym14061119"},{"key":"ref_5","first-page":"71","article-title":"A study on q-analogue of degenerate 12-Changhee numbers and polynomials","volume":"18","author":"Khan","year":"2022","journal-title":"South East Asian Math. Math. 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