DLMF:19.21.E11 (Q6429)

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DLMF:19.21.E11
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    Statements

    Defining formula
    6 ⁢ R G ⁡ ( x , y , z ) = 3 ⁢ ( x + y + z ) ⁢ R F ⁡ ( x , y , z ) - ∑ x 2 ⁢ R D ⁡ ( y , z , x ) = ∑ x ⁢ ( y + z ) ⁢ R D ⁡ ( y , z , x ) , 6 Carlson-integral-RG 𝑥 𝑦 𝑧 3 𝑥 𝑦 𝑧 Carlson-integral-RF 𝑥 𝑦 𝑧 superscript 𝑥 2 Carlson-integral-RD 𝑦 𝑧 𝑥 𝑥 𝑦 𝑧 Carlson-integral-RD 𝑦 𝑧 𝑥 {\displaystyle{\displaystyle 6R_{G}\left(x,y,z\right)=3(x+y+z)R_{F}\left(x,y,z% \right)-\sum x^{2}R_{D}\left(y,z,x\right)=\sum x(y+z)R_{D}\left(y,z,x\right),}}
    0 references
    DLMF id
    DLMF:19.21.E11
    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.m2ahdec
    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.m2aidec
    0 references
    symmetric elliptic integral of second kind
    Defining formula
    R G ⁡ ( x , y , z ) Carlson-integral-RG 𝑥 𝑦 𝑧 {\displaystyle{\displaystyle R_{G}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}
    xml-id
    C19.S16.E3.m2acdec
    0 references
     
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