DLMF:25.11.E38 (Q7712): Difference between revisions

Revision as of 13:45, 2 January 2020

No description defined

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

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

C25.S11.E1.m2aaldec

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

C1.S2.SS1.m1abdec

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

C5.S2.E2.m2addec

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@@ Property / Symbols used @@
+psi (or digamma) function
@@ Property / Symbols used: psi (or digamma) function / rank @@
+Normal rank
@@ Property / Symbols used: psi (or digamma) function / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}$ 
\digamma@{\NVar{z}}
@@ Property / Symbols used: psi (or digamma) function / qualifier @@
+xml-id: C5.S2.E2.m2addec