DLMF:32.11.E17 (Q9452)

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DLMF:32.11.E17
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    Statements

    Defining formula
    d 2 = π - 1 ⁢ ln ⁡ ( 1 + k 2 ) , superscript 𝑑 2 superscript 𝜋 1 1 superscript 𝑘 2 {\displaystyle{\displaystyle d^{2}=\pi^{-1}\ln\left(1+k^{2}\right),}}
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    DLMF id
    DLMF:32.11.E17
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    constraint
    sign ⁡ ( k ) = ( - 1 ) n sign 𝑘 superscript 1 𝑛 {\displaystyle{\displaystyle\operatorname{sign}\left(k\right)=(-1)^{n}}}
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    Symbols used
    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.m2agdec
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    Q10897
    Defining formula
    sign ⁡ x sign 𝑥 {\displaystyle{\displaystyle\operatorname{sign}\NVar{x}}}
    xml-id
    introduction.Sx4.p2.t1.r18.m6acdec
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    Q12571
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C32.S1.XMD2.m1adec
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    Q12534
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C32.S1.XMD5.m1fdec
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    Q12640
    Defining formula
    d 𝑑 {\displaystyle{\displaystyle d}}
    xml-id
    C32.S11.XMD9.m1cdec
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