DLMF:25.11.E18 (Q7692): 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.m2adec

Revision as of 13:39, 2 January 2020

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DLMF:25.11.E18
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    Statements

    Defining formula
    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 id
    DLMF:25.11.E18
    0 references
    constraint
    a > 0 𝑎 0 {\displaystyle{\displaystyle a>0}}
    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
    Hurwitz zeta function
    Defining formula
    ζ ⁡ ( s , a ) Hurwitz-zeta 𝑠 𝑎 {\displaystyle{\displaystyle\zeta\left(\NVar{s},\NVar{a}\right)}}
    xml-id
    C25.S11.E1.m2asdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
    0 references
    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2adec
    0 references
     
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