# Zeta function (chart) Calculator

## Calculates a table of the Riemann zeta functions ζ(x) and ζ(x)-1 and draws the chart.

 initial value x [ increment repetition ]
 $\normal Zeta\ function\ \zeta(x)\\[10](1)\ \zeta(x)= {\large\sum_{\small n=1}^ {\small\infty}\frac{1}{n^x}}\hspace{30}x\ge 1,\hspace{20}\zeta(1)=\infty\\(2)\ \zeta(2n)={\large\frac{2^{2n-1}\pi^{2n}|B_{2n}|}{(2n)!}}\hspace{30}{\normal n=1,2,3,...}\\(3)\ \zeta(-n)={\large\frac{B_{n+1}}{n+1}}\hspace{30}{\normal n=2,3,4,...}\\(4)\ \zeta(x)={\large\prod_{\small p:prime}\frac{1}{1-p^{-x}}}\hspace{30}{\normal Euler\ product}\\\hspace{120}B_n:Bernoulli\ number\\$

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