DLMF:20.9.E5 (Q6836)

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DLMF:20.9.E5
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    Statements

    Defining formula
    exp ⁡ ( - π ⁢ R F ⁡ ( 0 , k 2 , 1 ) R F ⁡ ( 0 , k ′ 2 , 1 ) ) = q . 𝜋 Carlson-integral-RF 0 superscript 𝑘 2 1 Carlson-integral-RF 0 superscript superscript 𝑘 ′ 2 1 𝑞 {\displaystyle{\displaystyle\exp\left(-\frac{\pi R_{F}\left(0,k^{2},1\right)}{% R_{F}\left(0,{k^{\prime}}^{2},1\right)}\right)=q.}}
    0 references
    DLMF id
    DLMF:20.9.E5
    0 references
    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.m2abdec
    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
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    exponential function
    Defining formula
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2adec
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    Q11950
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C20.S1.XMD5.m1bdec
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    modulus (locally)
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C20.S9.XMD3.m1bdec
    0 references
     
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