Formula:8188

Digital Library of Mathematical Functions ID 24.8.E8

${\displaystyle{\displaystyle\frac{B_{2n}}{4n}\left(\alpha^{n}-(-\beta)^{n}\right)=\alpha^{n}\sum_{k=1}^{\infty}\frac{k^{2n-1}}{e^{2\alpha k}-1}-(-\beta)^{n}\sum_{k=1}^{\infty}\frac{k^{2n-1}}{e^{2\beta k}-1},}}$

Constraint(s)

${\displaystyle{\displaystyle n=2,3,\dots}}$

Symbols List

• ${\displaystyle{\displaystyle B_{\NVar{n}}}}$:
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle k}}$: integer
• ${\displaystyle{\displaystyle n}}$: integer
• ${\displaystyle{\displaystyle\alpha}}$: parameter
• ${\displaystyle{\displaystyle\beta}}$: parameter
 

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