Riemann xi

The Riemann $\xi$ function is defined by the formula $$\xi(z)=\dfrac{z}{2}(z-1)\pi^{-\frac{z}{2}}\Gamma\left(\dfrac{z}{2}\right)\zeta(z),$$ where $\pi$ denotes pi, $\Gamma$ denotes gamma, and $\zeta$ denotes Riemann zeta.

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  Domain coloring of $\xi$.

Properties

Functional equation for Riemann xi

References

• 1930: Edward Charles Titchmarsh: The Zeta-Function of Riemann ... (previous) ... (next): § Introduction $(7)$