DLMF:25.11.E18 (Q7692): Difference between revisions

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Created a new Item: Wikidata Toolkit example test item creation
 
Changed an Item: Add constraint
 
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Property / constraint
 

a > 0 𝑎 0 {\displaystyle{\displaystyle a>0}}

a>0
Property / constraint: a > 0 𝑎 0 {\displaystyle{\displaystyle a>0}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: gamma function / rank
 
Normal rank
Property / Symbols used: gamma function / qualifier
 
Defining formula:

Γ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

\EulerGamma@{\NVar{z}}
Property / Symbols used: gamma function / qualifier
 
xml-id: C5.S2.E1.m2acdec
Property / Symbols used
 
Property / Symbols used: Hurwitz zeta function / rank
 
Normal rank
Property / Symbols used: Hurwitz zeta function / qualifier
 
Defining formula:

ζ ( s , a ) Hurwitz-zeta 𝑠 𝑎 {\displaystyle{\displaystyle\zeta\left(\NVar{s},\NVar{a}\right)}}

\Hurwitzzeta@{\NVar{s}}{\NVar{a}}
Property / Symbols used: Hurwitz zeta function / qualifier
 
xml-id: C25.S11.E1.m2asdec
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
 
Defining formula:

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.m2abdec
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.m2adec
Property / Symbols used
 
Property / Symbols used: Q12161 / rank
 
Normal rank
Property / Symbols used: Q12161 / qualifier
 
Defining formula:

a 𝑎 {\displaystyle{\displaystyle a}}

a
Property / Symbols used: Q12161 / qualifier
 
xml-id: C25.S1.XMD6.m1pdec

Latest revision as of 13:39, 2 January 2020

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DLMF:25.11.E18
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    Statements

    ζ ( 0 , a ) = ln Γ ( a ) - 1 2 ln ( 2 π ) , diffop Hurwitz-zeta 1 0 𝑎 Euler-Gamma 𝑎 1 2 2 𝜋 {\displaystyle{\displaystyle\zeta'\left(0,a\right)=\ln\Gamma\left(a\right)-% \tfrac{1}{2}\ln\left(2\pi\right),}}
    0 references
    DLMF:25.11.E18
    0 references
    a > 0 𝑎 0 {\displaystyle{\displaystyle a>0}}
    0 references
    Γ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    C5.S2.E1.m2acdec
    0 references
    ζ ( s , a ) Hurwitz-zeta 𝑠 𝑎 {\displaystyle{\displaystyle\zeta\left(\NVar{s},\NVar{a}\right)}}
    C25.S11.E1.m2asdec
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2abdec
    0 references
    ln z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    C4.S2.E2.m2adec
    0 references
    a 𝑎 {\displaystyle{\displaystyle a}}
    C25.S1.XMD6.m1pdec
    0 references