DLMF:19.24.E1 (Q6482)

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DLMF:19.24.E1
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    Statements

    Defining formula
    ln ⁡ 4 ≤ z ⁢ R F ⁡ ( 0 , y , z ) + ln ⁡ y / z ≤ 1 2 ⁢ π , 4 𝑧 Carlson-integral-RF 0 𝑦 𝑧 𝑦 𝑧 1 2 𝜋 {\displaystyle{\displaystyle\ln 4\leq\sqrt{z}R_{F}\left(0,y,z\right)+\ln\sqrt{% y/z}\leq\tfrac{1}{2}\pi,}}
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    DLMF id
    DLMF:19.24.E1
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    constraint
    0 < y ≤ z 0 𝑦 𝑧 {\displaystyle{\displaystyle 0<y\leq z}}
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    Symbols used
    symmetric elliptic integral of first kind
    Defining formula
    R F ⁡ ( x , y , z ) Carlson-integral-RF 𝑥 𝑦 𝑧 {\displaystyle{\displaystyle R_{F}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}
    xml-id
    C19.S16.E1.m2adec
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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.m2adec
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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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