Explicit, Determinantal, and Recurrent Formulas of Generalized Eulerian Polynomials
In the paper, by virtue of the Faà di Bruno formula, with the aid of some properties of the Bell polynomials of the second kind, and by means of a general formula for derivatives of the ratio between two differentiable functions, the authors establish explicit, determinantal, and recurrent formulas...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-03-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/10/1/37 |
| _version_ | 1797540817036902400 |
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| author | Yan Wang Muhammet Cihat Dağli Xi-Min Liu Feng Qi |
| author_facet | Yan Wang Muhammet Cihat Dağli Xi-Min Liu Feng Qi |
| author_sort | Yan Wang |
| collection | DOAJ |
| description | In the paper, by virtue of the Faà di Bruno formula, with the aid of some properties of the Bell polynomials of the second kind, and by means of a general formula for derivatives of the ratio between two differentiable functions, the authors establish explicit, determinantal, and recurrent formulas for generalized Eulerian polynomials. |
| first_indexed | 2024-03-10T13:06:25Z |
| format | Article |
| id | doaj.art-1444f25d1f0c4169b580f9e198475899 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-10T13:06:25Z |
| publishDate | 2021-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-1444f25d1f0c4169b580f9e1984758992023-11-21T11:04:06ZengMDPI AGAxioms2075-16802021-03-011013710.3390/axioms10010037Explicit, Determinantal, and Recurrent Formulas of Generalized Eulerian PolynomialsYan Wang0Muhammet Cihat Dağli1Xi-Min Liu2Feng Qi3School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, ChinaDepartment of Mathematics, Akdeniz University, Antalya 07058, TurkeySchool of Mathematical Sciences, Dalian University of Technology, Dalian 116024, ChinaInstitute of Mathematics, Henan Polytechnic University, Jiaozuo 454010, ChinaIn the paper, by virtue of the Faà di Bruno formula, with the aid of some properties of the Bell polynomials of the second kind, and by means of a general formula for derivatives of the ratio between two differentiable functions, the authors establish explicit, determinantal, and recurrent formulas for generalized Eulerian polynomials.https://www.mdpi.com/2075-1680/10/1/37Faà di Bruno formulageneralized Eulerian polynomialBell polynomial of the second kindgeneral formula for derivatives of the ratio between two differentiable functionsexplicit formuladeterminantal formula |
| spellingShingle | Yan Wang Muhammet Cihat Dağli Xi-Min Liu Feng Qi Explicit, Determinantal, and Recurrent Formulas of Generalized Eulerian Polynomials Axioms Faà di Bruno formula generalized Eulerian polynomial Bell polynomial of the second kind general formula for derivatives of the ratio between two differentiable functions explicit formula determinantal formula |
| title | Explicit, Determinantal, and Recurrent Formulas of Generalized Eulerian Polynomials |
| title_full | Explicit, Determinantal, and Recurrent Formulas of Generalized Eulerian Polynomials |
| title_fullStr | Explicit, Determinantal, and Recurrent Formulas of Generalized Eulerian Polynomials |
| title_full_unstemmed | Explicit, Determinantal, and Recurrent Formulas of Generalized Eulerian Polynomials |
| title_short | Explicit, Determinantal, and Recurrent Formulas of Generalized Eulerian Polynomials |
| title_sort | explicit determinantal and recurrent formulas of generalized eulerian polynomials |
| topic | Faà di Bruno formula generalized Eulerian polynomial Bell polynomial of the second kind general formula for derivatives of the ratio between two differentiable functions explicit formula determinantal formula |
| url | https://www.mdpi.com/2075-1680/10/1/37 |
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