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

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imported>Admin
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Property / constraint
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k = 1 , 2 , 3 , … π‘˜ 1 2 3 … {\displaystyle{\displaystyle k=1,2,3,\dots}}

k=1,2,3,\dots
Property / constraint: k = 1 , 2 , 3 , … π‘˜ 1 2 3 … {\displaystyle{\displaystyle k=1,2,3,\dots}} / rank
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Normal rank
Property / Symbols used
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Property / Symbols used: Hurwitz zeta function / rank
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Normal rank
Property / Symbols used: Hurwitz zeta function / qualifier
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test:

ΞΆ ⁑ ( s , a ) Hurwitz-zeta 𝑠 π‘Ž {\displaystyle{\displaystyle\zeta\left(\NVar{s},\NVar{a}\right)}}

\Hurwitzzeta@{\NVar{s}}{\NVar{a}}
Property / Symbols used: Hurwitz zeta function / qualifier
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xml-id: C25.S11.E1.m2aydec
Property / Symbols used
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Property / Symbols used: Riemann zeta function / rank
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Normal rank
Property / Symbols used: Riemann zeta function / qualifier
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test:

ΞΆ ⁑ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}

\Riemannzeta@{\NVar{s}}
Property / Symbols used: Riemann zeta function / qualifier
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xml-id: C25.S2.E1.m2afdec
Property / Symbols used
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Property / Symbols used: principal branch of logarithm function / rank
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Normal rank
Property / Symbols used: principal branch of logarithm function / qualifier
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test:

ln ⁑ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}

\ln@@{\NVar{z}}
Property / Symbols used: principal branch of logarithm function / qualifier
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xml-id: C4.S2.E2.m2afdec
Property / Symbols used
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Property / Symbols used: Q12161 / rank
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Normal rank
Property / Symbols used: Q12161 / qualifier
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test:

a π‘Ž {\displaystyle{\displaystyle a}}

a
Property / Symbols used: Q12161 / qualifier
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xml-id: C25.S1.XMD6.m1sdec
Property / Symbols used
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Property / Symbols used: Q12149 / rank
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Normal rank
Property / Symbols used: Q12149 / qualifier
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test:

s 𝑠 {\displaystyle{\displaystyle s}}

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

k π‘˜ {\displaystyle{\displaystyle k}}

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

Latest revision as of 12:41, 2 January 2020

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DLMF:25.11.E24
No description defined

    Statements

    test
    βˆ‘ r = 1 k - 1 ΞΆ β€² ⁑ ( s , r k ) = ( k s - 1 ) ⁒ ΞΆ β€² ⁑ ( s ) + k s ⁒ ΞΆ ⁑ ( s ) ⁒ ln ⁑ k , superscript subscript π‘Ÿ 1 π‘˜ 1 diffop Hurwitz-zeta 1 𝑠 π‘Ÿ π‘˜ superscript π‘˜ 𝑠 1 diffop Riemann-zeta 1 𝑠 superscript π‘˜ 𝑠 Riemann-zeta 𝑠 π‘˜ {\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 , … π‘˜ 1 2 3 … {\displaystyle{\displaystyle k=1,2,3,\dots}}
    0 references
    Symbols used
    Hurwitz zeta function
    test
    ΞΆ ⁑ ( s , a ) Hurwitz-zeta 𝑠 π‘Ž {\displaystyle{\displaystyle\zeta\left(\NVar{s},\NVar{a}\right)}}
    xml-id
    C25.S11.E1.m2aydec
    0 references
    Riemann zeta function
    test
    ΞΆ ⁑ ( 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 π‘Ž {\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 π‘˜ {\displaystyle{\displaystyle k}}
    xml-id
    C25.S11.XMD2.m1cdec
    0 references
     
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