DLMF:19.24.E15 (Q7196)

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DLMF:19.24.E15
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    Statements

    DLMF defining formula
    R C ⁡ ( x , 1 2 ⁢ ( y + z ) ) ≤ R F ⁡ ( x , y , z ) ≤ R C ⁡ ( x , y ⁢ z ) , Carlson-integral-RC 𝑥 1 2 𝑦 𝑧 Carlson-integral-RF 𝑥 𝑦 𝑧 Carlson-integral-RC 𝑥 𝑦 𝑧 {\displaystyle{\displaystyle R_{C}\left(x,\tfrac{1}{2}(y+z)\right)\leq R_{F}% \left(x,y,z\right)\leq R_{C}\left(x,\sqrt{yz}\right),}}
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    constraint
    x ≥ 0 𝑥 0 {\displaystyle{\displaystyle x\geq 0}}
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    Symbols used
    Carlson’s combination of inverse circular and inverse hyperbolic functions
    DLMF defining formula
    R C ⁡ ( x , y ) Carlson-integral-RC 𝑥 𝑦 {\displaystyle{\displaystyle R_{C}\left(\NVar{x},\NVar{y}\right)}}
    xml-id
    C19.S2.E17.m2adec
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    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
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