q-Genocchi Numbers and Polynomials Associated with Fermionic p-Adic Invariant Integrals on ℤp
The main purpose of this paper is to present a systemic study of some families of multiple Genocchi numbers and polynomials. In particular, by using the fermionic p-adic invariant integral on ℤp, we construct p-adic Genocchi numbers and polynomials of higher order. Finally, we derive the following i...
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| Format: | Article |
| Language: | English |
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Wiley
2008-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2008/232187 |
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| author | Leechae Jang Taekyun Kim |
| author_facet | Leechae Jang Taekyun Kim |
| author_sort | Leechae Jang |
| collection | DOAJ |
| description | The main purpose of this paper is to present a systemic study of some families of multiple Genocchi numbers and polynomials. In particular, by using the fermionic p-adic invariant integral on ℤp, we construct p-adic Genocchi numbers and polynomials of higher order. Finally, we derive the following interesting formula: Gn+k,q(k)(x)=2kk!(n+kk)∑l=0∞∑d0+d1+⋯+dk=k−1,di∈ℕ(−1)l(l+x)n, where Gn+k,q(k)(x) are the q-Genocchi polynomials of order k. |
| format | Article |
| id | doaj-art-391d5ad5567e4ec494e6e8fc77f0674d |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2008-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-391d5ad5567e4ec494e6e8fc77f0674d2025-02-03T07:24:34ZengWileyAbstract and Applied Analysis1085-33751687-04092008-01-01200810.1155/2008/232187232187q-Genocchi Numbers and Polynomials Associated with Fermionic p-Adic Invariant Integrals on ℤpLeechae Jang0Taekyun Kim1Department of Mathematics and Computer Science, KonKuk University, Chungju 380-701, South KoreaDivision of General Education-Mathematics, Kwangwoon University, Seoul 139-701, South KoreaThe main purpose of this paper is to present a systemic study of some families of multiple Genocchi numbers and polynomials. In particular, by using the fermionic p-adic invariant integral on ℤp, we construct p-adic Genocchi numbers and polynomials of higher order. Finally, we derive the following interesting formula: Gn+k,q(k)(x)=2kk!(n+kk)∑l=0∞∑d0+d1+⋯+dk=k−1,di∈ℕ(−1)l(l+x)n, where Gn+k,q(k)(x) are the q-Genocchi polynomials of order k.http://dx.doi.org/10.1155/2008/232187 |
| spellingShingle | Leechae Jang Taekyun Kim q-Genocchi Numbers and Polynomials Associated with Fermionic p-Adic Invariant Integrals on ℤp Abstract and Applied Analysis |
| title | q-Genocchi Numbers and Polynomials Associated with Fermionic p-Adic Invariant Integrals on ℤp |
| title_full | q-Genocchi Numbers and Polynomials Associated with Fermionic p-Adic Invariant Integrals on ℤp |
| title_fullStr | q-Genocchi Numbers and Polynomials Associated with Fermionic p-Adic Invariant Integrals on ℤp |
| title_full_unstemmed | q-Genocchi Numbers and Polynomials Associated with Fermionic p-Adic Invariant Integrals on ℤp |
| title_short | q-Genocchi Numbers and Polynomials Associated with Fermionic p-Adic Invariant Integrals on ℤp |
| title_sort | q genocchi numbers and polynomials associated with fermionic p adic invariant integrals on zp |
| url | http://dx.doi.org/10.1155/2008/232187 |
| work_keys_str_mv | AT leechaejang qgenocchinumbersandpolynomialsassociatedwithfermionicpadicinvariantintegralsonzp AT taekyunkim qgenocchinumbersandpolynomialsassociatedwithfermionicpadicinvariantintegralsonzp |