DLMF:25.11.E38 (Q7712)

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No description defined

Language	Label	Description	Also known as
English	DLMF:25.11.E38	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\sum_{k=1}^{\infty}\genfrac{(}{)}{0.0pt}{}{n+k}{k}% \zeta\left(n+k+1,a\right)z^{k}=\frac{(-1)^{n}}{n!}\left({\psi^{(n)}}\left(a% \right)-{\psi^{(n)}}\left(a-z\right)\right),}}

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DLMF:25.11.E38

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

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

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{\displaystyle{\displaystyle|z|<|a|}}

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Hurwitz zeta function

Defining formula

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

C25.S11.E1.m2aaldec

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Defining formula

{\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}

C1.S2.SS1.m1abdec

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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!}}

introduction.Sx4.p1.t1.r15.m5aedec

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Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1audec

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Defining formula

{\displaystyle{\displaystyle k}}

C25.S1.XMD1.m1hdec

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Defining formula

{\displaystyle{\displaystyle n}}

C25.S1.XMD3.m1udec

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Defining formula

{\displaystyle{\displaystyle a}}

C25.S1.XMD6.m1aedec

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Defining formula

{\displaystyle{\displaystyle z}}

C25.S1.XMD8.m1bdec

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Sitelinks

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