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Zeta Function

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Calculate the values of the Riemann zeta function ζ(x) and ζ(x)-1.
x
Real numbers
\(\normalsize Zeta\ function\ \zeta(x)\\ (1)\ \zeta(x)= {\large\displaystyle \sum_{\small n=1}^ {\small\infty}\frac{1}{n^x}}\hspace{30px}x\ge 1,\hspace{20px}\zeta(1)=\infty\\ (2)\ \zeta(2n)={\large\frac{2^{2n-1}\pi^{2n}|B_{2n}|}{(2n)!}}\hspace{30px}{\normalsize n=1,2,3,...}\\ (3)\ \zeta(-n)={\large - \frac{B_{n+1}}{n+1}}\hspace{30px}{\normalsize n=2,3,4,...}\\ (4)\ \zeta(x)={\large\prod_{\small p:prime}\frac{1}{1-p^{-x}}}\hspace{30px}{\normalsize Euler\ product}\\ \hspace{120px}B_n:Bernoulli\ number\\ \)

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