DLMF:25.11.E8 (Q7682)

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Language	Label	Description	Also known as
English	DLMF:25.11.E8	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\zeta\left(s,\tfrac{1}{2}a\right)=\zeta\left(s,% \tfrac{1}{2}a+\tfrac{1}{2}\right)+2^{s}\sum_{n=0}^{\infty}\frac{(-1)^{n}}{(n+a% )^{s}},}}

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DLMF:25.11.E8

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{\displaystyle{\displaystyle\Re s>0}}

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{\displaystyle{\displaystyle s\neq 1}}

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{\displaystyle{\displaystyle 0<a\leq 1}}

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Hurwitz zeta function

Defining formula

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

C25.S11.E1.m2aidec

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Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1addec

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Defining formula

{\displaystyle{\displaystyle n}}

C25.S1.XMD3.m1edec

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Defining formula

{\displaystyle{\displaystyle a}}

C25.S1.XMD6.m1hdec

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Defining formula

{\displaystyle{\displaystyle s}}

C25.S1.XMD7.m1gdec

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Sitelinks

Wikipedia(0 entries)

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