DLMF:25.8.E7 (Q7664): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: principal branch of logarithm function / rank
 
Normal rank
Property / Symbols used: principal branch of logarithm function / qualifier
 
Defining formula:

ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}

\ln@@{\NVar{z}}
Property / Symbols used: principal branch of logarithm function / qualifier
 
xml-id: C4.S2.E2.m2aadec

Revision as of 13:34, 2 January 2020

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DLMF:25.8.E7
No description defined

    Statements

    Defining formula
    ∑ k = 2 ∞ ζ ⁡ ( k ) k ⁢ z k = - γ ⁢ z + ln ⁡ Γ ⁡ ( 1 - z ) , superscript subscript 𝑘 2 Riemann-zeta 𝑘 𝑘 superscript 𝑧 𝑘 𝑧 Euler-Gamma 1 𝑧 {\displaystyle{\displaystyle\sum_{k=2}^{\infty}\frac{\zeta\left(k\right)}{k}z^% {k}=-\gamma z+\ln\Gamma\left(1-z\right),}}
    0 references
    DLMF id
    DLMF:25.8.E7
    0 references
    constraint
    | z | < 1 𝑧 1 {\displaystyle{\displaystyle|z|<1}}
    0 references
    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2acdec
    0 references
    Euler’s constant
    Defining formula
    γ {\displaystyle{\displaystyle\gamma}}
    xml-id
    C5.S2.E3.m2aadec
    0 references
    Riemann zeta function
    Defining formula
    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
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2aadec
    0 references
     
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