Formula:8300

Digital Library of Mathematical Functions ID 25.2.E12

${\displaystyle{\displaystyle\zeta\left(s\right)=\frac{(2\pi)^{s}e^{-s-(\gamma s/2)}}{2(s-1)\Gamma\left(\tfrac{1}{2}s+1\right)}\prod_{\rho}\left(1-\frac{s}{\rho}\right)e^{s/\rho},}}$

Symbols List

• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle\gamma}}$: Euler’s constant
• ${\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}$: Riemann zeta function
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle s}}$: complex variable
• ${\displaystyle{\displaystyle\rho}}$: zeros
 

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