Difference between revisions of "Riemann xi"
From specialfunctionswiki
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where $\Gamma$ denotes the [[gamma function]] and $\zeta$ denotes the [[Riemann zeta function]]. | where $\Gamma$ denotes the [[gamma function]] and $\zeta$ denotes the [[Riemann zeta function]]. | ||
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| + | File:Complex Riemann Xi.jpg|Domain coloring of $\xi$. | ||
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=Properties= | =Properties= | ||
| − | + | [[Functional equation for Riemann xi]]<br /> | |
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| − | + | =References= | |
| − | + | * {{BookReference|The Zeta-Function of Riemann|1930|Edward Charles Titchmarsh|prev=Functional equation for Riemann zeta with cosine|next=Functional equation for Riemann xi}}: § Introduction $(7)$ | |
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[[Category:SpecialFunction]] | [[Category:SpecialFunction]] | ||
Revision as of 15:19, 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 $\Gamma$ denotes the gamma function and $\zeta$ denotes the Riemann zeta function.
Domain coloring of $\xi$.
Properties
Functional equation for Riemann xi
References
- 1930: Edward Charles Titchmarsh: The Zeta-Function of Riemann ... (previous) ... (next): § Introduction $(7)$
