DLMF:25.5.E19 (Q7632)

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Language	Label	Description	Also known as
English	DLMF:25.5.E19	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\zeta\left(m+s\right)=(-1)^{m-1}\frac{\Gamma\left(% s\right)\sin\left(\pi s\right)}{\pi\Gamma\left(m+s\right)}\*\int_{0}^{\infty}{% \psi^{(m)}}\left(1+x\right)x^{-s}\mathrm{d}x,}}

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DLMF:25.5.E19

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{\displaystyle{\displaystyle m=1,2,3,\dots}}

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Defining formula

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

C5.S2.E1.m2aidec

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Riemann zeta function

Defining formula

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

C25.S2.E1.m2aqdec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2aidec

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Defining formula

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

C1.S4.SS4.m1aqdec

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psi (or digamma) function

Defining formula

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

C5.S2.E2.m2addec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3aqdec

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Sitelinks

Wikipedia(0 entries)

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