TY - JOUR A2 - Atici, Ferhan AU - Jang, Leechae AU - Kim, Taekyun PY - 2008 DA - 2008/05/13 TI - -Genocchi Numbers and Polynomials Associated with Fermionic -Adic Invariant Integrals on SP - 232187 VL - 2008 AB - The main purpose of this paper is to present a systemic study of somefamilies of multiple Genocchi numbers and polynomials. In particular, by using thefermionic p-adic invariant integral on p, we construct p-adic Genocchi numbers andpolynomials of higher order. Finally, we derive the following interesting formula: Gn+k,q(k)(x)=2kk!(n+kk)l=0d0+d1++dk=k1,di(1)l(l+x)n, where Gn+k,q(k)(x) are the q-Genocchi polynomials of order k. SN - 1085-3375 UR - https://doi.org/10.1155/2008/232187 DO - 10.1155/2008/232187 JF - Abstract and Applied Analysis PB - Hindawi Publishing Corporation KW - ER -