DLMF:2.6.E5 (Q830)

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DLMF:2.6.E5
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    Statements

    Defining formula
    ∫ 0 ∞ t - s - ( 1 / 3 ) x + t ⁢ d t = 2 ⁢ π 3 ⁢ ( - 1 ) s x s + ( 1 / 3 ) , superscript subscript 0 superscript 𝑡 𝑠 1 3 𝑥 𝑡 𝑡 2 𝜋 3 superscript 1 𝑠 superscript 𝑥 𝑠 1 3 {\displaystyle{\displaystyle\int_{0}^{\infty}\frac{t^{-s-(1/3)}}{x+t}\mathrm{d% }t=\frac{2\pi}{\sqrt{3}}\frac{(-1)^{s}}{x^{s+(1/3)}},}}
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    DLMF id
    DLMF:2.6.E5
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    constraint
    s = 0 , 1 , 2 , … 𝑠 0 1 2 … {\displaystyle{\displaystyle s=0,1,2,\dots}}
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1acdec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3acdec
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