DLMF:19.20.E19 (Q6410)

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DLMF:19.20.E19
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    Statements

    Defining formula
    R D ⁡ ( x , y , z ) ∼ 3 ⁢ ( x ⁢ y ⁢ z ) - 1 / 2 , asymptotically-equals Carlson-integral-RD 𝑥 𝑦 𝑧 3 superscript 𝑥 𝑦 𝑧 1 2 {\displaystyle{\displaystyle R_{D}\left(x,y,z\right)\sim 3(xyz)^{-1/2},}}
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    DLMF id
    DLMF:19.20.E19
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    constraint
    z / x ⁢ y → 0 → 𝑧 𝑥 𝑦 0 {\displaystyle{\displaystyle z/\sqrt{xy}\to 0}}
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    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.m2addec
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    asymptotic equality
    Defining formula
    ∼ asymptotically-equals {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.E1.m2aadec
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