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

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Property / Symbols used
 
Property / Symbols used: Q12149 / rank
 
Normal rank
Property / Symbols used: Q12149 / qualifier
 
test:

s 𝑠 {\displaystyle{\displaystyle s}}

s
Property / Symbols used: Q12149 / qualifier
 
xml-id: C25.S1.XMD7.m1pdec
Property / Symbols used
 
Property / Symbols used: Q12162 / rank
 
Normal rank
Property / Symbols used: Q12162 / qualifier
 
test:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q12162 / qualifier
 
xml-id: C25.S11.XMD2.m1cdec

Latest revision as of 12:41, 2 January 2020

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DLMF:25.11.E24
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    Statements

    test
    ∑ 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,}}
    0 references
    DLMF id
    DLMF:25.11.E24
    0 references
    constraint
    k = 1 , 2 , 3 , … 𝑘 1 2 3 … {\displaystyle{\displaystyle k=1,2,3,\dots}}
    0 references
    Symbols used
    Hurwitz zeta function
    test
    ζ ⁡ ( s , a ) Hurwitz-zeta 𝑠 𝑎 {\displaystyle{\displaystyle\zeta\left(\NVar{s},\NVar{a}\right)}}
    xml-id
    C25.S11.E1.m2aydec
    0 references
    Riemann zeta function
    test
    ζ ⁡ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}
    xml-id
    C25.S2.E1.m2afdec
    0 references
    principal branch of logarithm function
    test
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2afdec
    0 references
    Q12161
    test
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C25.S1.XMD6.m1sdec
    0 references
    Q12149
    test
    s 𝑠 {\displaystyle{\displaystyle s}}
    xml-id
    C25.S1.XMD7.m1pdec
    0 references
    Q12162
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C25.S11.XMD2.m1cdec
    0 references
     
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