DLMF:19.16.E5 (Q6320)

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DLMF:19.16.E5
No description defined

    Statements

    Defining formula
    R D ⁡ ( x , y , z ) = R J ⁡ ( x , y , z , z ) = 3 2 ⁢ ∫ 0 ∞ d t s ⁢ ( t ) ⁢ ( t + z ) , Carlson-integral-RD 𝑥 𝑦 𝑧 Carlson-integral-RJ 𝑥 𝑦 𝑧 𝑧 3 2 superscript subscript 0 𝑡 𝑠 𝑡 𝑡 𝑧 {\displaystyle{\displaystyle R_{D}\left(x,y,z\right)=R_{J}\left(x,y,z,z\right)% =\frac{3}{2}\int_{0}^{\infty}\frac{\mathrm{d}t}{s(t)(t+z)},}}
    0 references
    DLMF id
    DLMF:19.16.E5
    0 references
    Symbols used
    symmetric elliptic integral of third kind
    Defining formula
    R J ⁡ ( x , y , z , p ) Carlson-integral-RJ 𝑥 𝑦 𝑧 𝑝 {\displaystyle{\displaystyle R_{J}\left(\NVar{x},\NVar{y},\NVar{z},\NVar{p}% \right)}}
    xml-id
    C19.S16.E2.m2aadec
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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1acdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3acdec
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    Q11852
    Defining formula
    s ⁢ ( t ) 𝑠 𝑡 {\displaystyle{\displaystyle s(t)}}
    xml-id
    C19.S16.XMD1.m1cdec
    0 references
     
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