DLMF:19.20.E17 (Q6405): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: symmetric elliptic integral of third kind / rank
 
Normal rank
Property / Symbols used: symmetric elliptic integral of third kind / qualifier
 
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)}}

\CarlsonsymellintRJ@{\NVar{x}}{\NVar{y}}{\NVar{z}}{\NVar{p}}
Property / Symbols used: symmetric elliptic integral of third kind / qualifier
 
xml-id: C19.S16.E2.m2aidec

Latest revision as of 12:57, 2 January 2020

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DLMF:19.20.E17
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    Statements

    test
    ( 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),}}
    0 references
    DLMF id
    DLMF:19.20.E17
    0 references
    constraint
    w = z / ( z + q ) 𝑤 𝑧 𝑧 𝑞 {\displaystyle{\displaystyle w=z/(z+q)}}
    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.m2agdec
    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.m2aidec
    0 references
     
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