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) = 2 kk!(kn+k) Σl=0∞ Σd0+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. Copyright © 2008 L. Jang and T. Kim.
Jang, L., & Kim, T. (2008). q-Genocchi numbers and polynomials associated with fermionic p-adic invariant integrals on ℤp. Abstract and Applied Analysis, 2008. https://doi.org/10.1155/2008/232187