Formula:8176

Digital Library of Mathematical Functions ID 24.7.E7

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \BernoullipolyB{2n}@{x}=(-1)^{n+1}2n\*\int_{0}^{\infty}\frac{\cos@{2\pi x}-e^{-2\pi t}}{\cosh@{2\pi t}-\cos@{2\pi x}}t^{2n-1}\diff{t},}

Constraint(s)

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

Symbols List

• ${\displaystyle{\displaystyle B_{\NVar{n}}\left(\NVar{x}\right)}}$:
• ${\displaystyle{\displaystyle\pi}}$: 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
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\cosh\NVar{z}}}$: hyperbolic cosine function
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle n}}$: integer
• ${\displaystyle{\displaystyle t}}$: real or complex
• ${\displaystyle{\displaystyle x}}$: real or complex
 

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