DLMF:19.20.E9 (Q6393)

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DLMF:19.20.E9
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    Statements

    test
    R J ⁡ ( 0 , y , z , ± y ⁢ z ) = ± 3 2 ⁢ y ⁢ z ⁢ R F ⁡ ( 0 , y , z ) . Carlson-integral-RJ 0 𝑦 𝑧 plus-or-minus 𝑦 𝑧 plus-or-minus 3 2 𝑦 𝑧 Carlson-integral-RF 0 𝑦 𝑧 {\displaystyle{\displaystyle R_{J}\left(0,y,z,\pm\sqrt{yz}\right)=\pm\frac{3}{% 2\sqrt{yz}}R_{F}\left(0,y,z\right).}}
    0 references
    DLMF id
    DLMF:19.20.E9
    0 references
    Symbols used
    symmetric elliptic integral of first kind
    test
    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.m2acdec
    0 references
    symmetric elliptic integral of third kind
    test
    R J ⁡ ( x , y , z , p ) Carlson-integral-RJ 𝑥 𝑦 𝑧 𝑝 {\displaystyle{\displaystyle R_{J}\left(\NVar{x},\NVar{y},\NVar{z},\NVar{p}% \right)}}
    xml-id
    C19.S16.E2.m2acdec
    0 references
     
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