A Note on Some Identities of New Type Degenerate Bell Polynomials
Recently, the partially degenerate Bell polynomials and numbers, which are a degenerate version of Bell polynomials and numbers, were introduced. In this paper, we consider the new type degenerate Bell polynomials and numbers, and obtain several expressions and identities on those polynomials and nu...
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-11-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/7/11/1086 |
| _version_ | 1818934910755274752 |
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| author | Taekyun Kim Dae San Kim Hyunseok Lee Jongkyum Kwon |
| author_facet | Taekyun Kim Dae San Kim Hyunseok Lee Jongkyum Kwon |
| author_sort | Taekyun Kim |
| collection | DOAJ |
| description | Recently, the partially degenerate Bell polynomials and numbers, which are a degenerate version of Bell polynomials and numbers, were introduced. In this paper, we consider the new type degenerate Bell polynomials and numbers, and obtain several expressions and identities on those polynomials and numbers. In more detail, we obtain an expression involving the Stirling numbers of the second kind and the generalized falling factorial sequences, Dobinski type formulas, an expression connected with the Stirling numbers of the first and second kinds, and an expression involving the Stirling polynomials of the second kind. |
| first_indexed | 2024-12-20T05:11:47Z |
| format | Article |
| id | doaj.art-6390f84ed79f4cce8cb6dc598b21c6d0 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-12-20T05:11:47Z |
| publishDate | 2019-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-6390f84ed79f4cce8cb6dc598b21c6d02022-12-21T19:52:15ZengMDPI AGMathematics2227-73902019-11-01711108610.3390/math7111086math7111086A Note on Some Identities of New Type Degenerate Bell PolynomialsTaekyun Kim0Dae San Kim1Hyunseok Lee2Jongkyum Kwon3School of Science, Xi’an Technological University, Xi’an 710021, ChinaDepartment of Mathematics, Sogang University, Seoul 04107, KoreaDepartment of Mathematics, Kwangwoon University, Seoul 01897, KoreaDepartment of Mathematics Education and ERI, Gyeongsang National University, Gyeongsangnamdo 52828, KoreaRecently, the partially degenerate Bell polynomials and numbers, which are a degenerate version of Bell polynomials and numbers, were introduced. In this paper, we consider the new type degenerate Bell polynomials and numbers, and obtain several expressions and identities on those polynomials and numbers. In more detail, we obtain an expression involving the Stirling numbers of the second kind and the generalized falling factorial sequences, Dobinski type formulas, an expression connected with the Stirling numbers of the first and second kinds, and an expression involving the Stirling polynomials of the second kind.https://www.mdpi.com/2227-7390/7/11/1086bell polynomialspartially degenerate bell polynomialsnew type degenerate bell polynomials |
| spellingShingle | Taekyun Kim Dae San Kim Hyunseok Lee Jongkyum Kwon A Note on Some Identities of New Type Degenerate Bell Polynomials Mathematics bell polynomials partially degenerate bell polynomials new type degenerate bell polynomials |
| title | A Note on Some Identities of New Type Degenerate Bell Polynomials |
| title_full | A Note on Some Identities of New Type Degenerate Bell Polynomials |
| title_fullStr | A Note on Some Identities of New Type Degenerate Bell Polynomials |
| title_full_unstemmed | A Note on Some Identities of New Type Degenerate Bell Polynomials |
| title_short | A Note on Some Identities of New Type Degenerate Bell Polynomials |
| title_sort | note on some identities of new type degenerate bell polynomials |
| topic | bell polynomials partially degenerate bell polynomials new type degenerate bell polynomials |
| url | https://www.mdpi.com/2227-7390/7/11/1086 |
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