DLMF:19.21.E2 (Q6420): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: elliptic integral symmetric in only two variables / rank
 
Normal rank
Property / Symbols used: elliptic integral symmetric in only two variables / qualifier
 
test:

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

\CarlsonsymellintRD@{\NVar{x}}{\NVar{y}}{\NVar{z}}
Property / Symbols used: elliptic integral symmetric in only two variables / qualifier
 
xml-id: C19.S16.E5.m2aadec
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.m2aadec

Latest revision as of 12:58, 2 January 2020

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DLMF:19.21.E2
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    Statements

    test
    3 ⁢ R F ⁡ ( 0 , y , z ) = z ⁢ R D ⁡ ( 0 , y , z ) + y ⁢ R D ⁡ ( 0 , z , y ) . 3 Carlson-integral-RF 0 𝑦 𝑧 𝑧 Carlson-integral-RD 0 𝑦 𝑧 𝑦 Carlson-integral-RD 0 𝑧 𝑦 {\displaystyle{\displaystyle 3R_{F}\left(0,y,z\right)=zR_{D}\left(0,y,z\right)% +yR_{D}\left(0,z,y\right).}}
    0 references
    DLMF id
    DLMF:19.21.E2
    0 references
    Symbols used
    elliptic integral symmetric in only two variables
    test
    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.m2aadec
    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.m2aadec
    0 references
     
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