DLMF:25.11.E37 (Q7711): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:25.11.E37	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\sum_{k=1}^{\infty}\frac{(-1)^{k}}{k}\zeta\left(nk% ,a\right)=-n\ln\Gamma\left(a\right)+\ln\left(\prod_{j=0}^{n-1}\Gamma\left(a-e^% {(2j+1)\pi i/n}\right)\right),}}

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DLMF:25.11.E37

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{\displaystyle{\displaystyle\Re a\geq 1}}

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{\displaystyle{\displaystyle n=2,3,4,\dots}}

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{\displaystyle{\displaystyle\Re a\geq 1}}

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Defining formula

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

C5.S2.E1.m2ajdec

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Hurwitz zeta function

Defining formula

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

C25.S11.E1.m2aakdec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2agdec

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base of natural logarithm

Defining formula

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

C4.S2.E11.m2agdec

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Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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