Formula:8189

Digital Library of Mathematical Functions ID 24.8.E9

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle {}\EulernumberE{2n}=(-1)^{n}\sum_{k=1}^{\infty}\frac{k^{2n}}{\cosh@{\tfrac{1}{2}\pi k}}-4\sum_{k=0}^{\infty}\frac{(-1)^{k}(2k+1)^{2n}}{e^{2\pi(2k+1)}-1},}

Constraint(s)

${\displaystyle{\displaystyle n=1,2,\dots}}$

Symbols List

• ${\displaystyle{\displaystyle E_{\NVar{n}}}}$:
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\cosh\NVar{z}}}$: hyperbolic cosine function
• ${\displaystyle{\displaystyle k}}$: integer
• ${\displaystyle{\displaystyle n}}$: integer
 

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