View source for Functional equation for the zeta function

The '''functional equation for Riemann zeta function''' is a result due to analytic continuation of Riemann zeta function:

<cmath>
\zeta(s)=2^s\pi^{s-1}\sin\left(\pi s\over2\right)\Gamma(1-s)\zeta(1-s)
</cmath>

There are multiple proofs for the functional equation for Riemann zeta function, and this page presents a lightweighted approach which merely relies on Fourier series that

<cmath>
\frac12-\{x\}=\sum_{n=1}^\infty{\sin(2\pi nx)\over\pi n}
</cmath>