DLMF:19.22.E21 (Q6467)

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DLMF:19.22.E21
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    Statements

    Defining formula
    2 ⁢ R G ⁡ ( x 2 , y 2 , z 2 ) = 4 ⁢ R G ⁡ ( a 2 , z + 2 , z - 2 ) - x ⁢ y ⁢ R F ⁡ ( x 2 , y 2 , z 2 ) - z , 2 Carlson-integral-RG superscript 𝑥 2 superscript 𝑦 2 superscript 𝑧 2 4 Carlson-integral-RG superscript 𝑎 2 superscript subscript 𝑧 2 superscript subscript 𝑧 2 𝑥 𝑦 Carlson-integral-RF superscript 𝑥 2 superscript 𝑦 2 superscript 𝑧 2 𝑧 {\displaystyle{\displaystyle 2R_{G}\left(x^{2},y^{2},z^{2}\right)=4R_{G}\left(% a^{2},z_{+}^{2},z_{-}^{2}\right)-xyR_{F}\left(x^{2},y^{2},z^{2}\right)-z,}}
    0 references
    DLMF id
    DLMF:19.22.E21
    0 references
    Symbols used
    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
     
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