{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,26]],"date-time":"2026-04-26T09:57:09Z","timestamp":1777197429907,"version":"3.51.4"},"reference-count":28,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2019,8,14]],"date-time":"2019-08-14T00:00:00Z","timestamp":1565740800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea","doi-asserted-by":"publisher","award":["2017R1E1A1A03070882"],"award-info":[{"award-number":["2017R1E1A1A03070882"]}],"id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Recently, the degenerate    \u03bb   -Stirling polynomials of the second kind were introduced and investigated for their properties and relations. In this paper, we continue to study the degenerate    \u03bb   -Stirling polynomials as well as the r-truncated degenerate    \u03bb   -Stirling polynomials of the second kind which are derived from generating functions and Newton\u2019s formula. We derive recurrence relations and various expressions for them. Regarding applications, we show that both the degenerate    \u03bb   -Stirling polynomials of the second and the r-truncated degenerate    \u03bb   -Stirling polynomials of the second kind appear in the expressions of the probability distributions of appropriate random variables.<\/jats:p>","DOI":"10.3390\/sym11081046","type":"journal-article","created":{"date-parts":[[2019,8,14]],"date-time":"2019-08-14T03:59:26Z","timestamp":1565755166000},"page":"1046","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":28,"title":["Degenerate Stirling Polynomials of the Second Kind and Some Applications"],"prefix":"10.3390","volume":"11","author":[{"given":"Taekyun","family":"Kim","sequence":"first","affiliation":[{"name":"Department of Mathematics, Kwangwoon University, Seoul 139-701, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9599-7015","authenticated-orcid":false,"given":"Dae San","family":"Kim","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Sogang University, Seoul 121-742, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Han Young","family":"Kim","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Kwangwoon University, Seoul 139-701, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jongkyum","family":"Kwon","sequence":"additional","affiliation":[{"name":"Department of Mathematics Education and ERI, Gyeongsang National University, Jinju 52828, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,8,14]]},"reference":[{"key":"ref_1","first-page":"399","article-title":"A note on the Frobenius-Euler numbers and polynomials associated with Bernstein polynomials","volume":"22","author":"Araci","year":"2012","journal-title":"Adv. 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