DLMF:9.10.E5 (Q2887)

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DLMF:9.10.E5
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    Statements

    test
    ∫ 0 x Bi ⁡ ( t ) ⁢ d t ∼ π - 1 / 2 ⁢ x - 3 / 4 ⁢ exp ⁡ ( 2 3 ⁢ x 3 / 2 ) , asymptotically-equals superscript subscript 0 𝑥 Airy-Bi 𝑡 𝑡 superscript 𝜋 1 2 superscript 𝑥 3 4 2 3 superscript 𝑥 3 2 {\displaystyle{\displaystyle\int_{0}^{x}\mathrm{Bi}\left(t\right)\mathrm{d}t% \sim\pi^{-1/2}x^{-3/4}\exp\left(\tfrac{2}{3}x^{3/2}\right),}}
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    DLMF id
    DLMF:9.10.E5
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    constraint
    x → ∞ → 𝑥 {\displaystyle{\displaystyle x\rightarrow\infty}}
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    Symbols used
    Q11081
    test
    Bi ⁡ ( z ) Airy-Bi 𝑧 {\displaystyle{\displaystyle\mathrm{Bi}\left(\NVar{z}\right)}}
    xml-id
    C9.S2.SS1.m2aadec
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    asymptotic equality
    test
    ∼ asymptotically-equals {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.E1.m2aadec
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    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2addec
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    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1addec
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    exponential function
    test
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2aadec
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    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3addec
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    Q11382
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C9.S1.XMD2.m1adec
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