Formula:8326

Digital Library of Mathematical Functions ID 25.5.E20

${\displaystyle{\displaystyle\zeta\left(s\right)=\frac{\Gamma\left(1-s\right)}{2\pi i}\int_{-\infty}^{(0+)}\frac{z^{s-1}}{e^{-z}-1}\mathrm{d}z,}}$

Constraint(s)

${\displaystyle{\displaystyle s\neq 1,2,\dots}}$

Symbols List

• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}$: Riemann zeta function
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle s}}$: complex variable
• ${\displaystyle{\displaystyle z}}$: complex variable
 

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