DLMF:25.5.E11

MaRDI QIDQ8317

• Label: DLMF:25.5.E11

Digital Library of Mathematical Functions ID 25.5.E11

${\displaystyle{\displaystyle\zeta\left(s\right)=\frac{1}{2}+\frac{1}{s-1}+2\int_{0}^{\infty}\frac{\sin\left(s\operatorname{arctan}x\right)}{(1+x^{2})^{s/2}(e^{2\pi x}-1)}\mathrm{d}x.}}$

Symbols List

• ${\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}$: 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
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\operatorname{arctan}\NVar{z}}}$:
• ${\displaystyle{\displaystyle\sin\NVar{z}}}$: sine function
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle s}}$: complex variable
 

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