Difference between revisions of "Riemann xi"

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The Riemann $\xi$ function is defined by the formula
 
The Riemann $\xi$ function is defined by the formula
 
$$\xi(z)=\dfrac{z}{2}(z-1)\pi^{-\frac{z}{2}}\Gamma\left(\dfrac{z}{2}\right)\zeta(z),$$
 
$$\xi(z)=\dfrac{z}{2}(z-1)\pi^{-\frac{z}{2}}\Gamma\left(\dfrac{z}{2}\right)\zeta(z),$$
where $\Gamma$ denotes the [[gamma function]] and $\zeta$ denotes the [[Riemann zeta function]].
+
where $\pi$ denotes [[pi]], $\Gamma$ denotes [[gamma]], and $\zeta$ denotes [[Riemann zeta]].
  
 
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Latest revision as of 15:31, 18 March 2017

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.

Properties

Functional equation for Riemann xi

References