DLMF:19.21.E6 (Q6424): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
 
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
 
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)}}

\CarlsonsymellintRJ@{\NVar{x}}{\NVar{y}}{\NVar{z}}{\NVar{p}}
Property / Symbols used: symmetric elliptic integral of third kind / qualifier
 
xml-id: C19.S16.E2.m2adec

Latest revision as of 13:58, 2 January 2020

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DLMF:19.21.E6
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    Statements

    Defining formula
    ( r ⁢ p / z ) ⁢ R J ⁡ ( 0 , y , z , p ) = ( r - 1 ) ⁢ R F ⁡ ( 0 , y , z ) ⁢ R D ⁡ ( p , r ⁢ z , z ) + R D ⁡ ( 0 , y , z ) ⁢ R F ⁡ ( p , r ⁢ z , z ) , 𝑟 𝑝 𝑧 Carlson-integral-RJ 0 𝑦 𝑧 𝑝 𝑟 1 Carlson-integral-RF 0 𝑦 𝑧 Carlson-integral-RD 𝑝 𝑟 𝑧 𝑧 Carlson-integral-RD 0 𝑦 𝑧 Carlson-integral-RF 𝑝 𝑟 𝑧 𝑧 {\displaystyle{\displaystyle(\sqrt{rp}/z)R_{J}\left(0,y,z,p\right)={(r-1)}R_{F% }\left(0,y,z\right)R_{D}\left(p,rz,z\right)+R_{D}\left(0,y,z\right)R_{F}\left(% p,rz,z\right),}}
    0 references
    DLMF id
    DLMF:19.21.E6
    0 references
    constraint
    r = ( y - p ) / ( y - z ) > 0 𝑟 𝑦 𝑝 𝑦 𝑧 0 {\displaystyle{\displaystyle r=(y-p)/(y-z)>0}}
    0 references
    Symbols used
    elliptic integral symmetric in only two variables
    Defining formula
    R D ⁡ ( x , y , z ) Carlson-integral-RD 𝑥 𝑦 𝑧 {\displaystyle{\displaystyle R_{D}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}
    xml-id
    C19.S16.E5.m2acdec
    0 references
    symmetric elliptic integral of first kind
    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.m2aedec
    0 references
    symmetric elliptic integral of third kind
    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.m2adec
    0 references
     
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