DLMF:20.9.E4 (Q6835)

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DLMF:20.9.E4
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    Statements

    Defining formula
    R F ⁡ ( 0 , θ 3 4 ⁡ ( 0 , q ) , θ 4 4 ⁡ ( 0 , q ) ) = 1 2 ⁢ π , Carlson-integral-RF 0 Jacobi-theta 3 4 0 𝑞 Jacobi-theta 4 4 0 𝑞 1 2 𝜋 {\displaystyle{\displaystyle R_{F}\left(0,{\theta_{3}^{4}}\left(0,q\right),{% \theta_{4}^{4}}\left(0,q\right)\right)=\tfrac{1}{2}\pi,}}
    0 references
    DLMF id
    DLMF:20.9.E4
    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.m2aadec
    0 references
    Q11945
    Defining formula
    θ j ⁡ ( z , q ) Jacobi-theta 𝑗 𝑧 𝑞 {\displaystyle{\displaystyle\theta_{\NVar{j}}\left(\NVar{z},\NVar{q}\right)}}
    xml-id
    C20.S2.SS1.m2aadec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    0 references
    Q11950
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C20.S1.XMD5.m1adec
    0 references
     
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