Riemann Zeta Function

This calculator calculates the Riemann zeta function. The Riemann zeta function (from Bernhard Riemann) is a special mathematical function which plays an important role in analytical number theory.

Enter the argument x for the calculation. Then click the calculate button.

To read the individual values move the mouse over the graphic.

With a value of x = 1 the result is infinite. To display small values, the Y-scale is at ∞ limited to +/- 20

Formula for the Riemann zeta function

\(\displaystyle \zeta(x)=\sum_{n=1}^{\infty}\frac{1}{n^x}=\frac{1}{Γ(s)}\int_0^∞\frac{x^{s-1}}{e^x-1}dx \)

\(\displaystyle Γ(s)=\int_0^∞ x^{s-1}\hspace{8px} e^{-x}\hspace{8px} dx \)

\(\displaystyle x ≥ 1,\hspace{30px} \zeta(1)=\infty \)

A detailed description can be found at Wikipedia