DLMF:9.5.E1 (Q3471)

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DLMF:9.5.E1
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    Statements

    DLMF defining formula
    Ai ⁡ ( x ) = 1 π ⁢ ∫ 0 ∞ cos ⁡ ( 1 3 ⁢ t 3 + x ⁢ t ) ⁢ d t . Airy-Ai 𝑥 1 𝜋 superscript subscript 0 1 3 superscript 𝑡 3 𝑥 𝑡 𝑡 {\displaystyle{\displaystyle\mathrm{Ai}\left(x\right)=\frac{1}{\pi}\int_{0}^{% \infty}\cos\left(\tfrac{1}{3}t^{3}+xt\right)\mathrm{d}t.}}
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    Symbols used
    Q10893
    DLMF defining formula
    Ai ⁡ ( z ) Airy-Ai 𝑧 {\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}
    xml-id
    C9.S2.SS1.m1adec
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    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
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    cosine function
    DLMF defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2adec
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    differential of x
    DLMF defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1adec
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    integral
    DLMF defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3adec
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    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C9.S1.XMD2.m1dec
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    Identifiers

     
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