DLMF:25.11.E34 (Q7708)

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Language	Label	Description	Also known as
English	DLMF:25.11.E34	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle n\int_{0}^{a}\zeta'\left(1-n,x\right)\mathrm{d}x=% \zeta'\left(-n,a\right)-\zeta'\left(-n\right)+\frac{B_{n+1}-B_{n+1}\left(a% \right)}{n(n+1)},}}

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DLMF:25.11.E34

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{\displaystyle{\displaystyle\Re a>0}}

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

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{\displaystyle{\displaystyle\Re a>0}}

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Defining formula

{\displaystyle{\displaystyle B_{\NVar{n}}}}

C24.S2.SS1.m1aidec

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Defining formula

{\displaystyle{\displaystyle B_{\NVar{n}}\left(\NVar{x}\right)}}

C24.S2.SS1.m2abdec

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Hurwitz zeta function

Defining formula

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

C25.S11.E1.m2aahdec

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Riemann zeta function

Defining formula

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

C25.S2.E1.m2ahdec

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Defining formula

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

C1.S4.SS4.m1amdec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3amdec

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Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1aqdec

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Sitelinks

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