DLMF:9.10.E13 (Q2896)

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DLMF:9.10.E13
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    Statements

    Defining formula
    ∫ - ∞ ∞ e p ⁢ t ⁢ Ai ⁡ ( t ) ⁢ d t = e p 3 / 3 , superscript subscript superscript 𝑒 𝑝 𝑡 Airy-Ai 𝑡 𝑡 superscript 𝑒 superscript 𝑝 3 3 {\displaystyle{\displaystyle\int_{-\infty}^{\infty}e^{pt}\mathrm{Ai}\left(t% \right)\mathrm{d}t=e^{p^{3}/3},}}
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    DLMF id
    DLMF:9.10.E13
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    constraint
    ℜ ⁡ p > 0 𝑝 0 {\displaystyle{\displaystyle\Re p>0}}
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    Symbols used
    Q10919
    Defining formula
    Ai ⁡ ( z ) Airy-Ai 𝑧 {\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}
    xml-id
    C9.S2.SS1.m1aedec
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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aldec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
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