# Formula:DLMF:25.5:E12

$\displaystyle {\displaystyle \RiemannZeta@{s} = \frac{2^{s-1}}{s-1} - 2^s \int_0^\infty \frac{\sin@{s \atan@@{x}}}{(1 + x^2)^{s/2} (\expe^{\cpi x} + 1)} \diff{x} }$

## Constraint(s)

$\displaystyle {\displaystyle s \neq 1}$

## Proof

We ask users to provide proof(s), reference(s) to proof(s), or further clarification on the proof(s) in this space.

## Symbols List

$\displaystyle {\displaystyle \zeta}$  : Riemann zeta function : http://dlmf.nist.gov/25.2#E1
$\displaystyle {\displaystyle \int}$  : integral : http://dlmf.nist.gov/1.4#iv
$\displaystyle {\displaystyle \mathrm{sin}}$  : sine function : http://dlmf.nist.gov/4.14#E1
$\displaystyle {\displaystyle \mathrm{arctan}}$  : inverse tangent function : http://dlmf.nist.gov/4.23#SS2.p1
$\displaystyle {\displaystyle \mathrm{e}}$  : the base of the natural logarithm : http://dlmf.nist.gov/4.2.E11
$\displaystyle {\displaystyle \pi}$  : ratio of a circle's circumference to its diameter : http://dlmf.nist.gov/5.19.E4
$\displaystyle {\displaystyle \mathrm{d}^nx}$  : differential : http://dlmf.nist.gov/1.4#iv