DLMF:2.10.E6 (Q993): 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.m2abdec

Revision as of 17:33, 1 January 2020

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DLMF:2.10.E6
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    Statements

    Defining formula
    C = γ + ln ⁡ ( 2 ⁢ π ) 12 - ζ ′ ⁡ ( 2 ) 2 ⁢ π 2 = 1 12 - ζ ′ ⁡ ( - 1 ) , 𝐶 2 𝜋 12 diffop Riemann-zeta 1 2 2 superscript 𝜋 2 1 12 diffop Riemann-zeta 1 1 {\displaystyle{\displaystyle C=\frac{\gamma+\ln\left(2\pi\right)}{12}-\frac{% \zeta'\left(2\right)}{2\pi^{2}}=\frac{1}{12}-\zeta'\left(-1\right),}}
    0 references
    DLMF id
    DLMF:2.10.E6
    0 references
    Symbols used
    Euler’s constant
    Defining formula
    γ {\displaystyle{\displaystyle\gamma}}
    xml-id
    C5.S2.E3.m2adec
    0 references
    Riemann zeta function
    Defining formula
    ζ ⁡ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}
    xml-id
    C25.S2.E1.m2adec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    0 references
    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2abdec
    0 references
     
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