DLMF:9.5.E2 (Q3472)

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DLMF:9.5.E2
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    Statements

    DLMF defining formula
    Ai ⁡ ( - x ) = x 1 / 2 π ⁢ ∫ - 1 ∞ cos ⁡ ( x 3 / 2 ⁢ ( 1 3 ⁢ t 3 + t 2 - 2 3 ) ) ⁢ d t , Airy-Ai 𝑥 superscript 𝑥 1 2 𝜋 superscript subscript 1 superscript 𝑥 3 2 1 3 superscript 𝑡 3 superscript 𝑡 2 2 3 𝑡 {\displaystyle{\displaystyle\mathrm{Ai}\left(-x\right)=\frac{x^{\ifrac{1}{2}}}% {\pi}\int_{-1}^{\infty}\cos\left(x^{\ifrac{3}{2}}(\tfrac{1}{3}t^{3}+t^{2}-% \tfrac{2}{3})\right)\mathrm{d}t,}}
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    constraint
    x > 0 𝑥 0 {\displaystyle{\displaystyle x>0}}
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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.m1aadec
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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.m2aadec
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    cosine function
    DLMF defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2aadec
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    differential of x
    DLMF defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aadec
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    integral
    DLMF defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aadec
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    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C9.S1.XMD2.m1adec
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    Identifiers

     
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