DLMF:25.11.E24 (Q7698): Difference between revisions

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Property / constraint
 

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

k=1,2,3,\dots
Property / constraint: k = 1 , 2 , 3 , 𝑘 1 2 3 {\displaystyle{\displaystyle k=1,2,3,\dots}} / rank
 
Normal rank

Revision as of 17:16, 30 December 2019

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DLMF:25.11.E24
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    r = 1 k - 1 ζ ( s , r k ) = ( k s - 1 ) ζ ( s ) + k s ζ ( s ) ln k , superscript subscript 𝑟 1 𝑘 1 diffop Hurwitz-zeta 1 𝑠 𝑟 𝑘 superscript 𝑘 𝑠 1 diffop Riemann-zeta 1 𝑠 superscript 𝑘 𝑠 Riemann-zeta 𝑠 𝑘 {\displaystyle{\displaystyle\sum_{r=1}^{k-1}\zeta'\left(s,\frac{r}{k}\right)=(% k^{s}-1)\zeta'\left(s\right)+k^{s}\zeta\left(s\right)\ln k,}}
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    k = 1 , 2 , 3 , 𝑘 1 2 3 {\displaystyle{\displaystyle k=1,2,3,\dots}}
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