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DLMF:19.21.E7 - MaRDI portal

DLMF:19.21.E7 (Q7121)

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DLMF:19.21.E7
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    Statements

    DLMF defining formula
    ( x - y ) ⁢ R D ⁡ ( y , z , x ) + ( z - y ) ⁢ R D ⁡ ( x , y , z ) = 3 ⁢ R F ⁡ ( x , y , z ) - 3 ⁢ y / ( x ⁢ z ) , 𝑥 𝑦 Carlson-integral-RD 𝑦 𝑧 𝑥 𝑧 𝑦 Carlson-integral-RD 𝑥 𝑦 𝑧 3 Carlson-integral-RF 𝑥 𝑦 𝑧 3 𝑦 𝑥 𝑧 {\displaystyle{\displaystyle(x-y)R_{D}\left(y,z,x\right)+(z-y)R_{D}\left(x,y,z% \right)=3R_{F}\left(x,y,z\right)-3\sqrt{y/(xz)},}}
    0 references
    Symbols used
    elliptic integral symmetric in only two variables
    DLMF 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.m2addec
    0 references
    symmetric elliptic integral of first kind
    DLMF 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.m2afdec
    0 references

    Identifiers

     
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