DLMF:25.5.E6 (Q7619)

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Language	Label	Description	Also known as
English	DLMF:25.5.E6	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\zeta\left(s\right)=\frac{1}{2}+\frac{1}{s-1}+% \frac{1}{\Gamma\left(s\right)}\int_{0}^{\infty}\left(\frac{1}{e^{x}-1}-\frac{1% }{x}+\frac{1}{2}\right)\frac{x^{s-1}}{e^{x}}\mathrm{d}x,}}

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DLMF:25.5.E6

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{\displaystyle{\displaystyle\Re s>-1}}

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Defining formula

{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

C5.S2.E1.m2addec

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Riemann zeta function

Defining formula

{\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}

C25.S2.E1.m2aedec

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Defining formula

{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

C1.S4.SS4.m1aedec

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base of natural logarithm

Defining formula

{\displaystyle{\displaystyle\mathrm{e}}}

C4.S2.E11.m2addec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3aedec

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Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1aedec

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Defining formula

{\displaystyle{\displaystyle x}}

C25.S1.XMD5.m1edec

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Sitelinks

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