DLMF:25.6.E6

MaRDI QIDQ8336

• Label: DLMF:25.6.E6

Digital Library of Mathematical Functions ID 25.6.E6

${\displaystyle{\displaystyle\zeta\left(2k+1\right)=\frac{(-1)^{k+1}(2\pi)^{2k+1}}{2(2k+1)!}\int_{0}^{1}B_{2k+1}\left(t\right)\cot\left(\pi t\right)\mathrm{d}t,}}$

Constraint(s)

${\displaystyle{\displaystyle k=1,2,3,\dots}}$

Symbols List

• ${\displaystyle{\displaystyle B_{\NVar{n}}\left(\NVar{x}\right)}}$:
• ${\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}$: Riemann zeta function
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\cot\NVar{z}}}$: cotangent function
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
 

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