DLMF:9.5.E4 (Q2776)

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DLMF:9.5.E4
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    Defining formula
    Ai ⁡ ( z ) = 1 2 ⁢ π ⁢ i ⁢ ∫ ∞ ⁢ e - π ⁢ i / 3 ∞ ⁢ e π ⁢ i / 3 exp ⁡ ( 1 3 ⁢ t 3 - z ⁢ t ) ⁢ d t , Airy-Ai 𝑧 1 2 𝜋 𝑖 superscript subscript superscript 𝑒 𝜋 𝑖 3 superscript 𝑒 𝜋 𝑖 3 1 3 superscript 𝑡 3 𝑧 𝑡 𝑡 {\displaystyle{\displaystyle\mathrm{Ai}\left(z\right)=\frac{1}{2\pi i}\int_{% \infty e^{-\pi i/3}}^{\infty e^{\pi i/3}}\exp\left(\tfrac{1}{3}t^{3}-zt\right)% \mathrm{d}t,}}
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    DLMF id
    DLMF:9.5.E4
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