DLMF:19.22.E7 (Q6445): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: symmetric elliptic integral of first kind / rank
 
Normal rank
Property / Symbols used: symmetric elliptic integral of first kind / qualifier
 
test:

R F ⁡ ( x , y , z ) Carlson-integral-RF 𝑥 𝑦 𝑧 {\displaystyle{\displaystyle R_{F}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}

\CarlsonsymellintRF@{\NVar{x}}{\NVar{y}}{\NVar{z}}
Property / Symbols used: symmetric elliptic integral of first kind / qualifier
 
xml-id: C19.S16.E1.m2addec
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.m2aadec

Latest revision as of 12:59, 2 January 2020

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DLMF:19.22.E7
No description defined

    Statements

    test
    2 ⁢ p 2 ⁢ R J ⁡ ( 0 , x 2 , y 2 , p 2 ) = v + ⁢ v - ⁢ R J ⁡ ( 0 , x ⁢ y , a 2 , v + 2 ) + 3 ⁢ R F ⁡ ( 0 , x ⁢ y , a 2 ) , 2 superscript 𝑝 2 Carlson-integral-RJ 0 superscript 𝑥 2 superscript 𝑦 2 superscript 𝑝 2 subscript 𝑣 subscript 𝑣 Carlson-integral-RJ 0 𝑥 𝑦 superscript 𝑎 2 subscript superscript 𝑣 2 3 Carlson-integral-RF 0 𝑥 𝑦 superscript 𝑎 2 {\displaystyle{\displaystyle 2p^{2}R_{J}\left(0,x^{2},y^{2},p^{2}\right)=v_{+}% v_{-}R_{J}\left(0,xy,a^{2},v^{2}_{+}\right)+3R_{F}\left(0,xy,a^{2}\right),}}
    0 references
    DLMF id
    DLMF:19.22.E7
    0 references
    constraint
    v ± = ( p 2 ± x ⁢ y ) / ( 2 ⁢ p ) subscript 𝑣 plus-or-minus plus-or-minus superscript 𝑝 2 𝑥 𝑦 2 𝑝 {\displaystyle{\displaystyle v_{\pm}=(p^{2}\pm xy)/(2p)}}
    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.m2addec
    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.m2aadec
    0 references
     
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