DLMF:25.11.E21 (Q7695): Difference between revisions

Revision as of 13:40, 2 January 2020

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Language	Label	Description	Also known as
English	DLMF:25.11.E21	No description defined

{\displaystyle{\displaystyle\zeta'\left(1-2n,\frac{h}{k}\right)=\frac{(\psi% \left(2n\right)-\ln\left(2\pi k\right))B_{2n}\left(h/k\right)}{2n}-\frac{(\psi% \left(2n\right)-\ln\left(2\pi\right))B_{2n}}{2nk^{2n}}+\frac{(-1)^{n+1}\pi}{(2% \pi k)^{2n}}\sum_{r=1}^{k-1}\sin\left(\frac{2\pi rh}{k}\right){\psi^{(2n-1)}}% \left(\frac{r}{k}\right)+\frac{(-1)^{n+1}2\cdot(2n-1)!}{(2\pi k)^{2n}}\sum_{r=% 1}^{k-1}\cos\left(\frac{2\pi rh}{k}\right)\zeta'\left(2n,\frac{r}{k}\right)+% \frac{\zeta'\left(1-2n\right)}{k^{2n}},}}

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DLMF:25.11.E21

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{\displaystyle{\displaystyle B_{\NVar{n}}}}

C24.S2.SS1.m1addec

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{\displaystyle{\displaystyle B_{\NVar{n}}\left(\NVar{x}\right)}}

C24.S2.SS1.m2aadec

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

C25.S11.E1.m2avdec

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@@ Property / Symbols used @@
+Hurwitz zeta function
@@ Property / Symbols used: Hurwitz zeta function / rank @@
+Normal rank
@@ Property / Symbols used: Hurwitz zeta function / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\zeta\left(\NVar{s},\NVar{a}\right)}}$ 
\Hurwitzzeta@{\NVar{s}}{\NVar{a}}
@@ Property / Symbols used: Hurwitz zeta function / qualifier @@
+xml-id: C25.S11.E1.m2avdec