DLMF:19.22.E3 (Q6438)

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DLMF:19.22.E3
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    Statements

    Defining formula
    2 ⁢ y 2 ⁢ R D ⁡ ( 0 , x 2 , y 2 ) = 1 4 ⁢ ( y 2 - x 2 ) ⁢ R D ⁡ ( 0 , x ⁢ y , a 2 ) + 3 ⁢ R F ⁡ ( 0 , x ⁢ y , a 2 ) . 2 superscript 𝑦 2 Carlson-integral-RD 0 superscript 𝑥 2 superscript 𝑦 2 1 4 superscript 𝑦 2 superscript 𝑥 2 Carlson-integral-RD 0 𝑥 𝑦 superscript 𝑎 2 3 Carlson-integral-RF 0 𝑥 𝑦 superscript 𝑎 2 {\displaystyle{\displaystyle 2y^{2}R_{D}\left(0,x^{2},y^{2}\right)=\tfrac{1}{4% }(y^{2}-x^{2})R_{D}\left(0,xy,a^{2}\right)+3R_{F}\left(0,xy,a^{2}\right).}}
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    DLMF id
    DLMF:19.22.E3
    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.m2adec
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    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.m2abdec
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