Abstract
In this paper, we study the Genoochi-zeta functions which are entire functions in whole complex s-plane these zeta functions have the values of the Genocchi numbers and the Genoochi polynomials at negative integers respectively. That is <TEX>${\zeta}_G(1-k)={\frac{G_k}{k}}$</TEX> and <TEX>${\zeta}_G(1-k,x)={\frac{G_k(x)}{k}}$</TEX>.
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