DLMF:9.10.E18 (Q2901)

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DLMF:9.10.E18
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    Statements

    Defining formula
    Ai ⁡ ( z ) = 3 ⁢ z 5 / 4 ⁢ e - ( 2 / 3 ) ⁢ z 3 / 2 4 ⁢ π ⁢ ∫ 0 ∞ t - 3 / 4 ⁢ e - ( 2 / 3 ) ⁢ t 3 / 2 ⁢ Ai ⁡ ( t ) z 3 / 2 + t 3 / 2 ⁢ d t , Airy-Ai 𝑧 3 superscript 𝑧 5 4 superscript 𝑒 2 3 superscript 𝑧 3 2 4 𝜋 superscript subscript 0 superscript 𝑡 3 4 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{3z^{5/4}e^{-(2/3)z% ^{3/2}}}{4\pi}\*\int_{0}^{\infty}\frac{t^{-3/4}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 id
    DLMF:9.10.E18
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    constraint
    | ph ⁡ z | < 2 3 ⁢ π phase 𝑧 2 3 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|<\tfrac{2}{3}\pi}}
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