q‐Genocchi Numbers and Polynomials Associated with Fermionic p‐Adic Invariant Integrals on ℤp

Leechae Jang and Taekyun Kim

Abstract and Applied Analysis, 2008, vol. 2008, issue 1

Abstract: 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.

Date: 2008
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https://doi.org/10.1155/2008/232187

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2008:y:2008:i:1:n:232187

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