DLMF:2.10.E6 (Q993): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Riemann zeta function / rank
 
Normal rank
Property / Symbols used: Riemann zeta function / qualifier
 
test:

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

\Riemannzeta@{\NVar{s}}
Property / Symbols used: Riemann zeta function / qualifier
 
xml-id: C25.S2.E1.m2adec
Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
test:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2aadec
Property / Symbols used
 
Property / Symbols used: principal branch of logarithm function / rank
 
Normal rank
Property / Symbols used: principal branch of logarithm function / qualifier
 
test:

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
Property / Symbols used
 
Property / Symbols used: Q11116 / rank
 
Normal rank
Property / Symbols used: Q11116 / qualifier
 
test:

C 𝐶 {\displaystyle{\displaystyle C}}

C
Property / Symbols used: Q11116 / qualifier
 
xml-id: C2.S10.XMD6.m1adec

Latest revision as of 17:34, 1 January 2020

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DLMF:2.10.E6
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    Statements

    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),}}
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    γ {\displaystyle{\displaystyle\gamma}}
    C5.S2.E3.m2adec
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    ζ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}
    C25.S2.E1.m2adec
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2aadec
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    ln z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    C4.S2.E2.m2abdec
    0 references
    C 𝐶 {\displaystyle{\displaystyle C}}
    C2.S10.XMD6.m1adec
    0 references