DLMF:27.4.E13 (Q8024): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q12234 / rank
 
Normal rank
Property / Symbols used: Q12234 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q12234 / qualifier
 
xml-id: C27.S1.XMD4.m1ldec

Latest revision as of 13:18, 2 January 2020

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DLMF:27.4.E13
No description defined

    Statements

    test
    ∑ n = 2 ∞ ( ln ⁡ n ) ⁢ n - s = - ζ ′ ⁡ ( s ) , superscript subscript 𝑛 2 𝑛 superscript 𝑛 𝑠 diffop Riemann-zeta 1 𝑠 {\displaystyle{\displaystyle\sum_{n=2}^{\infty}(\ln n)n^{-s}=-\zeta'\left(s% \right),}}
    0 references
    DLMF id
    DLMF:27.4.E13
    0 references
    constraint
    ℜ ⁡ s > 1 𝑠 1 {\displaystyle{\displaystyle\Re s>1}}
    0 references
    Symbols used
    Riemann zeta function
    test
    ζ ⁡ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}
    xml-id
    C25.S2.E1.m2aidec
    0 references
    principal branch of logarithm function
    test
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2adec
    0 references
    Q10811
    test
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1aidec
    0 references
    Q12234
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C27.S1.XMD4.m1ldec
    0 references
     
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