DLMF:19.29.E23 (Q6651)

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DLMF:19.29.E23
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    Statements

    Defining formula
    ∫ y ∞ d t ( t 2 + a 2 ) ⁢ ( t 2 - b 2 ) = R F ⁡ ( y 2 + a 2 , y 2 - b 2 , y 2 ) . superscript subscript 𝑦 𝑡 superscript 𝑡 2 superscript 𝑎 2 superscript 𝑡 2 superscript 𝑏 2 Carlson-integral-RF superscript 𝑦 2 superscript 𝑎 2 superscript 𝑦 2 superscript 𝑏 2 superscript 𝑦 2 {\displaystyle{\displaystyle\int_{y}^{\infty}\frac{\mathrm{d}t}{\sqrt{(t^{2}+a% ^{2})(t^{2}-b^{2})}}=R_{F}\left(y^{2}+a^{2},y^{2}-b^{2},y^{2}\right).}}
    0 references
    DLMF id
    DLMF:19.29.E23
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    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.m2abdec
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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1ahdec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3ahdec
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