First Functional Equation
\zeta(s)=2(2\pi)^{s-1}\sin\left(\frac{\pi}{2}s\right)\Gamma(1-s)\zeta(1-s)
The First Functional Equation for the Riemann Zeta is one of the classics that come directly from Riemann’s original paper.
It’s the first method used to expand the function to the whole complex plane, and to this day, it stands as one of the most essential relations concerning this function. Key to the demonstration is the Analytic continuation for 0<Re(s)<1.
Any questions?
Feel free to contact our authors at: [email protected], you will be put directly in touch with the person who wrote the text.
Didn’t find what you were looking for? Keep looking through all our formulas regarding the Riemann Zeta Function!
