Formula:8316

Digital Library of Mathematical Functions ID 25.5.E10

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

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
• ${\displaystyle{\displaystyle\cos\NVar{z}}}$: cosine function
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\cosh\NVar{z}}}$: hyperbolic cosine function
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\operatorname{arctan}\NVar{z}}}$:
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle s}}$: complex variable
 

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