DLMF:25.11.E5 (Q7679)

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Language	Label	Description	Also known as
English	DLMF:25.11.E5	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\zeta\left(s,a\right)=\sum_{n=0}^{N}\frac{1}{(n+a)% ^{s}}+\frac{(N+a)^{1-s}}{s-1}-s\int_{N}^{\infty}\frac{x-\left\lfloor x\right% \rfloor}{(x+a)^{s+1}}\mathrm{d}x,}}

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DLMF:25.11.E5

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

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{\displaystyle{\displaystyle a>0}}

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{\displaystyle{\displaystyle N=0,1,2,3,\dots}}

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Hurwitz zeta function

Defining formula

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

C25.S11.E1.m2afdec

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Defining formula

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

C1.S4.SS4.m1adec

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Defining formula

{\displaystyle{\displaystyle\left\lfloor\NVar{x}\right\rfloor}}

introduction.Sx4.p1.t1.r17.m4adec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3adec

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Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1aadec

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Defining formula

{\displaystyle{\displaystyle n}}

C25.S1.XMD3.m1cdec

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Defining formula

{\displaystyle{\displaystyle x}}

C25.S1.XMD5.m1bdec

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Defining formula

{\displaystyle{\displaystyle a}}

C25.S1.XMD6.m1edec

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Defining formula

{\displaystyle{\displaystyle s}}

C25.S1.XMD7.m1ddec

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