DLMF:19.20.E17 (Q7101)

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DLMF:19.20.E17
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    Statements

    DLMF defining formula
    ( q + z ) ⁢ R J ⁡ ( 0 , y , z , - q ) = ( p - z ) ⁢ R J ⁡ ( 0 , y , z , p ) - 3 ⁢ R F ⁡ ( 0 , y , z ) , 𝑞 𝑧 Carlson-integral-RJ 0 𝑦 𝑧 𝑞 𝑝 𝑧 Carlson-integral-RJ 0 𝑦 𝑧 𝑝 3 Carlson-integral-RF 0 𝑦 𝑧 {\displaystyle{\displaystyle(q+z)R_{J}\left(0,y,z,-q\right)=(p-z)R_{J}\left(0,% y,z,p\right)-3R_{F}\left(0,y,z\right),}}
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    constraint
    w = z / ( z + q ) 𝑤 𝑧 𝑧 𝑞 {\displaystyle{\displaystyle w=z/(z+q)}}
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    Symbols used
    symmetric elliptic integral of first kind
    DLMF 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.m2agdec
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    symmetric elliptic integral of third kind
    DLMF defining formula
    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.m2aidec
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    Identifiers

     
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