Symmetry Fermionic 𝑝-Adic 𝑞-Integral on ℤ𝑝 for Eulerian Polynomials
Kim et al. (2012) introduced an interesting p-adic analogue of the Eulerian polynomials. They studied some identities on the Eulerian polynomials in connection with the Genocchi, Euler, and tangent numbers. In this paper, by applying the symmetry of the fermionic p-adic q-integral on ℤ𝑝, defined by...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2012/424189 |
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| _version_ | 1832567593055027200 |
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| author | Daeyeoul Kim Min-Soo Kim |
| author_facet | Daeyeoul Kim Min-Soo Kim |
| author_sort | Daeyeoul Kim |
| collection | DOAJ |
| description | Kim et al. (2012) introduced an interesting p-adic analogue of the
Eulerian polynomials. They studied some identities on the Eulerian polynomials in
connection with the Genocchi, Euler, and tangent numbers. In this paper, by
applying the symmetry of the fermionic p-adic q-integral on ℤ𝑝, defined by
Kim (2008), we show a
symmetric relation between the q-extension of the alternating sum of integer
powers and the Eulerian polynomials. |
| format | Article |
| id | doaj-art-752f50915987429a8bcba504af10e9dd |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-752f50915987429a8bcba504af10e9dd2025-02-03T01:01:11ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252012-01-01201210.1155/2012/424189424189Symmetry Fermionic 𝑝-Adic 𝑞-Integral on ℤ𝑝 for Eulerian PolynomialsDaeyeoul Kim0Min-Soo Kim1National Institute for Mathematical Sciences, Yuseong-daero 1689-gil, Yuseong-gu, Daejeon 305-811, Republic of KoreaDivision of Cultural Education, Kyungnam University, Changwon 631-701, Republic of KoreaKim et al. (2012) introduced an interesting p-adic analogue of the Eulerian polynomials. They studied some identities on the Eulerian polynomials in connection with the Genocchi, Euler, and tangent numbers. In this paper, by applying the symmetry of the fermionic p-adic q-integral on ℤ𝑝, defined by Kim (2008), we show a symmetric relation between the q-extension of the alternating sum of integer powers and the Eulerian polynomials.http://dx.doi.org/10.1155/2012/424189 |
| spellingShingle | Daeyeoul Kim Min-Soo Kim Symmetry Fermionic 𝑝-Adic 𝑞-Integral on ℤ𝑝 for Eulerian Polynomials International Journal of Mathematics and Mathematical Sciences |
| title | Symmetry Fermionic 𝑝-Adic 𝑞-Integral on ℤ𝑝 for Eulerian Polynomials |
| title_full | Symmetry Fermionic 𝑝-Adic 𝑞-Integral on ℤ𝑝 for Eulerian Polynomials |
| title_fullStr | Symmetry Fermionic 𝑝-Adic 𝑞-Integral on ℤ𝑝 for Eulerian Polynomials |
| title_full_unstemmed | Symmetry Fermionic 𝑝-Adic 𝑞-Integral on ℤ𝑝 for Eulerian Polynomials |
| title_short | Symmetry Fermionic 𝑝-Adic 𝑞-Integral on ℤ𝑝 for Eulerian Polynomials |
| title_sort | symmetry fermionic 𝑝 adic 𝑞 integral on z𝑝 for eulerian polynomials |
| url | http://dx.doi.org/10.1155/2012/424189 |
| work_keys_str_mv | AT daeyeoulkim symmetryfermionicpadicqintegralonzpforeulerianpolynomials AT minsookim symmetryfermionicpadicqintegralonzpforeulerianpolynomials |