DLMF:19.20.E13 (Q6398)

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DLMF:19.20.E13
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    Statements

    test
    2 ⁢ ( p - x ) ⁢ R J ⁡ ( x , y , z , p ) = 3 ⁢ R F ⁡ ( x , y , z ) - 3 ⁢ x ⁢ R C ⁡ ( y ⁢ z , p 2 ) , 2 𝑝 𝑥 Carlson-integral-RJ 𝑥 𝑦 𝑧 𝑝 3 Carlson-integral-RF 𝑥 𝑦 𝑧 3 𝑥 Carlson-integral-RC 𝑦 𝑧 superscript 𝑝 2 {\displaystyle{\displaystyle 2(p-x)R_{J}\left(x,y,z,p\right)=3R_{F}\left(x,y,z% \right)-3\sqrt{x}R_{C}\left(yz,p^{2}\right),}}
    0 references
    DLMF id
    DLMF:19.20.E13
    0 references
    constraint
    p = x ± ( y - x ) ⁢ ( z - x ) 𝑝 plus-or-minus 𝑥 𝑦 𝑥 𝑧 𝑥 {\displaystyle{\displaystyle p=x\pm\sqrt{(y-x)(z-x)}}}
    0 references
    Symbols used
    Carlson’s combination of inverse circular and inverse hyperbolic functions
    test
    R C ⁡ ( x , y ) Carlson-integral-RC 𝑥 𝑦 {\displaystyle{\displaystyle R_{C}\left(\NVar{x},\NVar{y}\right)}}
    xml-id
    C19.S2.E17.m2addec
    0 references
    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.m2aedec
    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.m2agdec
    0 references
     
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