DLMF:19.29.E4 (Q6623)

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DLMF:19.29.E4
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    Statements

    Defining formula
    ∫ y x d t s ⁢ ( t ) = 2 ⁢ R F ⁡ ( U 12 2 , U 13 2 , U 23 2 ) , superscript subscript 𝑦 𝑥 𝑡 𝑠 𝑡 2 Carlson-integral-RF superscript subscript 𝑈 12 2 superscript subscript 𝑈 13 2 superscript subscript 𝑈 23 2 {\displaystyle{\displaystyle\int_{y}^{x}\frac{\mathrm{d}t}{s(t)}=2R_{F}\left(U% _{12}^{2},U_{13}^{2},U_{23}^{2}\right),}}
    0 references
    DLMF id
    DLMF:19.29.E4
    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.m2adec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1adec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3adec
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    Q11899
    Defining formula
    U n subscript 𝑈 𝑛 {\displaystyle{\displaystyle U_{n}}}
    xml-id
    C19.S29.XMD10.m1dec
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    Q11898
    Defining formula
    s ⁢ ( t ) 𝑠 𝑡 {\displaystyle{\displaystyle s(t)}}
    xml-id
    C19.S29.XMD4.m1adec
    0 references
     
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