Analytic Continuation for 0<Re(s)<1
\zeta(s)=-s\int_{0}^{\infty}\frac{x-[x]-\frac{1}{2}}{x^{s+1}}dx
This Formula is an unusual analytic continuation for the Riemann Zeta function for negative values of s.
It is at the core of the proof for the First Functional Equation.
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