Two Parametric Kinds of Eulerian-Type Polynomials Associated with Euler’s Formula
The purpose of this article is to construct generating functions for new families of special polynomials including two parametric kinds of Eulerian-type polynomials. Some fundamental properties of these functions are given. By using these generating functions and the Euler’s formula, some...
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-09-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/11/9/1097 |
| _version_ | 1818001802190127104 |
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| author | Neslihan Kilar Yilmaz Simsek |
| author_facet | Neslihan Kilar Yilmaz Simsek |
| author_sort | Neslihan Kilar |
| collection | DOAJ |
| description | The purpose of this article is to construct generating functions for new families of special polynomials including two parametric kinds of Eulerian-type polynomials. Some fundamental properties of these functions are given. By using these generating functions and the Euler’s formula, some identities and relations among trigonometric functions, two parametric kinds of Eulerian-type polynomials, Apostol-type polynomials, the Stirling numbers and Fubini-type polynomials are presented. Computational formulae for these polynomials are obtained. Applying a partial derivative operator to these generating functions, some derivative formulae and finite combinatorial sums involving the aforementioned polynomials and numbers are also obtained. In addition, some remarks and observations on these polynomials are given. |
| first_indexed | 2024-04-14T03:37:57Z |
| format | Article |
| id | doaj.art-c79dbbfb1c3e4f508c8921a08a304acc |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-14T03:37:57Z |
| publishDate | 2019-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-c79dbbfb1c3e4f508c8921a08a304acc2022-12-22T02:14:40ZengMDPI AGSymmetry2073-89942019-09-01119109710.3390/sym11091097sym11091097Two Parametric Kinds of Eulerian-Type Polynomials Associated with Euler’s FormulaNeslihan Kilar0Yilmaz Simsek1Department of Mathematics, Faculty of Science, University of Akdeniz, TR-07058 Antalya, TurkeyDepartment of Mathematics, Faculty of Science, University of Akdeniz, TR-07058 Antalya, TurkeyThe purpose of this article is to construct generating functions for new families of special polynomials including two parametric kinds of Eulerian-type polynomials. Some fundamental properties of these functions are given. By using these generating functions and the Euler’s formula, some identities and relations among trigonometric functions, two parametric kinds of Eulerian-type polynomials, Apostol-type polynomials, the Stirling numbers and Fubini-type polynomials are presented. Computational formulae for these polynomials are obtained. Applying a partial derivative operator to these generating functions, some derivative formulae and finite combinatorial sums involving the aforementioned polynomials and numbers are also obtained. In addition, some remarks and observations on these polynomials are given.https://www.mdpi.com/2073-8994/11/9/1097Apostol-type numbers and polynomialsStirling numberscombinatorial sumgenerating functionspecial functions |
| spellingShingle | Neslihan Kilar Yilmaz Simsek Two Parametric Kinds of Eulerian-Type Polynomials Associated with Euler’s Formula Symmetry Apostol-type numbers and polynomials Stirling numbers combinatorial sum generating function special functions |
| title | Two Parametric Kinds of Eulerian-Type Polynomials Associated with Euler’s Formula |
| title_full | Two Parametric Kinds of Eulerian-Type Polynomials Associated with Euler’s Formula |
| title_fullStr | Two Parametric Kinds of Eulerian-Type Polynomials Associated with Euler’s Formula |
| title_full_unstemmed | Two Parametric Kinds of Eulerian-Type Polynomials Associated with Euler’s Formula |
| title_short | Two Parametric Kinds of Eulerian-Type Polynomials Associated with Euler’s Formula |
| title_sort | two parametric kinds of eulerian type polynomials associated with euler s formula |
| topic | Apostol-type numbers and polynomials Stirling numbers combinatorial sum generating function special functions |
| url | https://www.mdpi.com/2073-8994/11/9/1097 |
| work_keys_str_mv | AT neslihankilar twoparametrickindsofeuleriantypepolynomialsassociatedwitheulersformula AT yilmazsimsek twoparametrickindsofeuleriantypepolynomialsassociatedwitheulersformula |