Second Functional Equation - Positive Increment

Second Functional Equation

\zeta(1-s)\equal2(2\pi)^{-s}\cos\left(\frac{\pi}{2}s\right)\Gamma(s)\zeta(s)

The Second functional equation for the Riemann Zeta is a direct corollary of the First Functional Equation.

While simple to obtain, it retains some intriguing implications.

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Analytic continuation for 0 — Analytic continuation for 0<Re s<1

Laurent Expansion

Euler's Product Formula

First Derivative

Xi Reflection Formula

Relation to the Gamma Function 1

See all Formulas for the Riemann Zeta…