DLMF:25.16.E6 (Q7761)

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Language	Label	Description	Also known as
English	DLMF:25.16.E6	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle H\left(s\right)=-\zeta'\left(s\right)+\gamma\zeta% \left(s\right)+\frac{1}{2}\zeta\left(s+1\right)+\sum_{r=1}^{k}\zeta\left(1-2r% \right)\zeta\left(s+2r\right)+\sum_{n=1}^{\infty}\frac{1}{n^{s}}\int_{n}^{% \infty}\frac{\widetilde{B}_{2k+1}\left(x\right)}{x^{2k+2}}\mathrm{d}x,}}

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DLMF:25.16.E6

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Euler’s constant

Defining formula

{\displaystyle{\displaystyle\gamma}}

C5.S2.E3.m2adec

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Defining formula

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

C25.S16.SS2.p1.m1aadec

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Riemann zeta function

Defining formula

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

C25.S2.E1.m2aadec

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Defining formula

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

C1.S4.SS4.m1adec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3adec

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Defining formula

{\displaystyle{\displaystyle\widetilde{B}_{\NVar{n}}\left(\NVar{x}\right)}}

C24.S2.SS3.m1adec

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Defining formula

{\displaystyle{\displaystyle k}}

C25.S1.XMD1.m1dec

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Defining formula

{\displaystyle{\displaystyle n}}

C25.S1.XMD3.m1adec

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Defining formula

{\displaystyle{\displaystyle x}}

C25.S1.XMD5.m1ddec

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Defining formula

{\displaystyle{\displaystyle s}}

C25.S1.XMD7.m1adec

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Sitelinks

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