{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,1]],"date-time":"2026-02-01T03:32:43Z","timestamp":1769916763794,"version":"3.49.0"},"reference-count":14,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2022,7,22]],"date-time":"2022-07-22T00:00:00Z","timestamp":1658448000000},"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>The main aim of this study is to define degenerate Genocchi polynomials and numbers of the second kind by using logarithmic functions, and to investigate some of their analytical properties and some applications. For this purpose, many formulas and relations for these polynomials, including some implicit summation formulas, differentiation rules and correlations with the earlier polynomials by utilizing some series manipulation methods, are derived. Additionally, as an application, the zero values of degenerate Genocchi polynomials and numbers of the second kind are presented in tables and multifarious graphical representations for these zero values are shown.<\/jats:p>","DOI":"10.3390\/sym14081500","type":"journal-article","created":{"date-parts":[[2022,7,22]],"date-time":"2022-07-22T03:58:44Z","timestamp":1658462324000},"page":"1500","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Analytical Properties of Degenerate Genocchi Polynomials of the Second Kind and Some of Their Applications"],"prefix":"10.3390","volume":"14","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":[[2022,7,22]]},"reference":[{"key":"ref_1","first-page":"51","article-title":"Degenerate Stirling Bernoulli and Eulerian numbers","volume":"15","author":"Carlitz","year":"1979","journal-title":"Util. Math."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1007\/BF01900520","article-title":"A degenerate Staud-Clausen theorem","volume":"7","author":"Carlitz","year":"1956","journal-title":"Arch. Math."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1269","DOI":"10.12988\/ijma.2015.5260","article-title":"Degenerate Bernoulli numbers and polynomials of the second kind","volume":"9","author":"Kim","year":"2015","journal-title":"Int. J. Math. Anal."},{"key":"ref_4","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_5","doi-asserted-by":"crossref","first-page":"587","DOI":"10.1186\/s13662-020-03055-4","article-title":"New construction of type 2 of degenerate central Fubini polynomials with their certain properties","volume":"2020","author":"Sharma","year":"2020","journal-title":"Adv. Differ. 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(Kyngshang)"},{"key":"ref_10","first-page":"651","article-title":"Degenerate Bernoulli numbers and polynomials associated with degenerate Hermite polynomials","volume":"33","author":"Haroon","year":"2018","journal-title":"Commun. Korean Math. Soc."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1134\/S1061920809010063","article-title":"Symmetry of power sum polynomials and multivariate fermionic p-adic invariant integral on Zp","volume":"16","author":"Kim","year":"2009","journal-title":"Russ. J. Math. Phys."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"569","DOI":"10.4134\/BKMS.2016.53.2.569","article-title":"Some identities of degenerate Genocchi polynomials","volume":"53","author":"Lim","year":"2016","journal-title":"Bull. Korean Math. Soc."},{"key":"ref_13","first-page":"4789","article-title":"On the generalized partially degenerate Genocchi polynomials","volume":"11","author":"Jang","year":"2015","journal-title":"Glob. J. Pure Appl. Math."},{"key":"ref_14","unstructured":"Maryam, S.A., and Khan, W.A. (Axioms, 2022). New type of degenerate Changhee-Genocchi polynomials, Axioms, accepted."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/8\/1500\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:54:34Z","timestamp":1760140474000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/8\/1500"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7,22]]},"references-count":14,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2022,8]]}},"alternative-id":["sym14081500"],"URL":"https:\/\/doi.org\/10.3390\/sym14081500","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,7,22]]}}}