DLMF:25.5.E8

MaRDI QIDQ8314

• Label: DLMF:25.5.E8

Digital Library of Mathematical Functions ID 25.5.E8

${\displaystyle{\displaystyle\zeta\left(s\right)=\frac{1}{2(1-2^{-s})\Gamma\left(s\right)}\int_{0}^{\infty}\frac{x^{s-1}}{\sinh x}\mathrm{d}x,}}$

Constraint(s)

${\displaystyle{\displaystyle\Re s>1}}$

Symbols List

• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}$: Riemann zeta function
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\sinh\NVar{z}}}$: hyperbolic sine function
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\Re}}$: real part
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle s}}$: complex variable
 

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