DLMF:9.5.E5 (Q2777)

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DLMF:9.5.E5
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    Bi ( z ) = 1 2 π - e π i / 3 exp ( 1 3 t 3 - z t ) d t + 1 2 π - e - π i / 3 exp ( 1 3 t 3 - z t ) d t . Airy-Bi 𝑧 1 2 𝜋 superscript subscript superscript 𝑒 𝜋 𝑖 3 1 3 superscript 𝑡 3 𝑧 𝑡 𝑡 1 2 𝜋 superscript subscript superscript 𝑒 𝜋 𝑖 3 1 3 superscript 𝑡 3 𝑧 𝑡 𝑡 {\displaystyle{\displaystyle\mathrm{Bi}\left(z\right)=\frac{1}{2\pi}\int_{-% \infty}^{\infty e^{\pi i/3}}\exp\left(\tfrac{1}{3}t^{3}-zt\right)\mathrm{d}t+% \dfrac{1}{2\pi}\int_{-\infty}^{\infty e^{-\pi i/3}}\exp\left(\tfrac{1}{3}t^{3}% -zt\right)\mathrm{d}t.}}
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    DLMF:9.5.E5
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