DLMF:19.29.E32 (Q6671)

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DLMF:19.29.E32
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    Statements

    Defining formula
    ∫ y x d t t 4 + a 4 = 2 ⁢ R F ⁡ ( U , U + 2 ⁢ a 2 , U - 2 ⁢ a 2 ) , superscript subscript 𝑦 𝑥 𝑡 superscript 𝑡 4 superscript 𝑎 4 2 Carlson-integral-RF 𝑈 𝑈 2 superscript 𝑎 2 𝑈 2 superscript 𝑎 2 {\displaystyle{\displaystyle\int_{y}^{x}\frac{\mathrm{d}t}{\sqrt{t^{4}+a^{4}}}% =2R_{F}\left(U,U+2a^{2},U-2a^{2}\right),}}
    0 references
    DLMF id
    DLMF:19.29.E32
    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.m2afdec
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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aldec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aldec
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    Q11908
    Defining formula
    U 𝑈 {\displaystyle{\displaystyle U}}
    xml-id
    C19.S29.XMD16.m1jdec
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