DLMF:9.10#Ex3 (Q2902)

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DLMF:9.10#Ex3
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    Ai ( z ) = z 5 / 4 e - ( 2 / 3 ) z 3 / 2 2 7 / 2 π 0 t - 1 / 2 e - ( 2 / 3 ) t 3 / 2 Ai ( t ) z 3 / 2 + t 3 / 2 d t Airy-Ai 𝑧 superscript 𝑧 5 4 superscript 𝑒 2 3 superscript 𝑧 3 2 superscript 2 7 2 𝜋 superscript subscript 0 superscript 𝑡 1 2 superscript 𝑒 2 3 superscript 𝑡 3 2 Airy-Ai 𝑡 superscript 𝑧 3 2 superscript 𝑡 3 2 𝑡 {\displaystyle{\displaystyle\mathrm{Ai}\left(z\right)=\frac{z^{5/4}e^{-(2/3)z^% {3/2}}}{2^{7/2}\pi}\*\int_{0}^{\infty}\frac{t^{-1/2}e^{-(2/3)t^{3/2}}\mathrm{% Ai}\left(t\right)}{z^{3/2}+t^{3/2}}\mathrm{d}t}}
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    DLMF:9.10#Ex3
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