DLMF:25.6.E11 (Q7648)

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DLMF:25.6.E11
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    Statements

    Defining formula
    ζ ′ ⁡ ( 0 ) = - 1 2 ⁢ ln ⁡ ( 2 ⁢ π ) . diffop Riemann-zeta 1 0 1 2 2 𝜋 {\displaystyle{\displaystyle\zeta'\left(0\right)=-\tfrac{1}{2}\ln\left(2\pi% \right).}}
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    DLMF id
    DLMF:25.6.E11
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    Symbols used
    Riemann zeta function
    Defining formula
    ζ ⁡ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}
    xml-id
    C25.S2.E1.m2ajdec
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    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2acdec
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    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2adec
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