DLMF:25.11.E27 (Q7701)

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Language	Label	Description	Also known as
English	DLMF:25.11.E27	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\zeta\left(s,a\right)=\frac{1}{2}a^{-s}+\frac{a^{1% -s}}{s-1}+\frac{1}{\Gamma\left(s\right)}\int_{0}^{\infty}\left(\frac{1}{e^{x}-% 1}-\frac{1}{x}+\frac{1}{2}\right)\frac{x^{s-1}}{e^{ax}}\mathrm{d}x,}}

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DLMF:25.11.E27

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{\displaystyle{\displaystyle\Re s>-1}}

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

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{\displaystyle{\displaystyle\Re s>-1}}

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

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

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Defining formula

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

C5.S2.E1.m2aedec

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Hurwitz zeta function

Defining formula

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

C25.S11.E1.m2aabdec

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Defining formula

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

C1.S4.SS4.m1agdec

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base of natural logarithm

Defining formula

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

C4.S2.E11.m2aadec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3agdec

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Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1akdec

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Defining formula

{\displaystyle{\displaystyle x}}

C25.S1.XMD5.m1idec

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Defining formula

{\displaystyle{\displaystyle a}}

C25.S1.XMD6.m1vdec

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Defining formula

{\displaystyle{\displaystyle s}}

C25.S1.XMD7.m1sdec

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Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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