DLMF:19.23.E3 (Q6474)

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DLMF:19.23.E3
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    Statements

    test
    R D ⁡ ( 0 , y , z ) = 3 ⁢ ∫ 0 π / 2 ( y ⁢ cos 2 ⁡ θ + z ⁢ sin 2 ⁡ θ ) - 3 / 2 ⁢ sin 2 ⁡ θ ⁢ d θ . Carlson-integral-RD 0 𝑦 𝑧 3 superscript subscript 0 𝜋 2 superscript 𝑦 2 𝜃 𝑧 2 𝜃 3 2 2 𝜃 𝜃 {\displaystyle{\displaystyle R_{D}\left(0,y,z\right)=3\int_{0}^{\pi/2}(y{\cos^% {2}}\theta+z{\sin^{2}}\theta)^{-3/2}{\sin^{2}}\theta\mathrm{d}\theta.}}
    0 references
    DLMF id
    DLMF:19.23.E3
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    Symbols used
    elliptic integral symmetric in only two variables
    test
    R D ⁡ ( x , y , z ) Carlson-integral-RD 𝑥 𝑦 𝑧 {\displaystyle{\displaystyle R_{D}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}
    xml-id
    C19.S16.E5.m2adec
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    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
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