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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 Ã¢Â„Â¤p, 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)Ã¢ÂˆÂ‘l=0Ã¢ÂˆÂžÃ¢ÂˆÂ‘d0+d1+Ã¢Â‹Â¯+dk=kÃ¢ÂˆÂ’1,diÃ¢ÂˆÂˆÃ¢Â„Â•(Ã¢ÂˆÂ’1)l(l+x)n, where Gn+k,q(k)(x) are the q-Genocchi polynomials of order k

abstract and applied analysis

<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>q</mml:mi></mml:math>-Genocchi Numbers and Polynomials Associated with Fermionic<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>p</mml:mi></mml:math>-Adic Invariant Integrals on<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>ℤ</mml:mi><mml:mi>p</mml:mi></mml:msub></mml:math>

q-Genocchi Numbers and Polynomials Associated with Fermionicp-Adic Invariant Integrals onℤp