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DLMF:9.10#Ex4 - MaRDI portal

DLMF:9.10#Ex4 (Q3602)

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DLMF:9.10#Ex4
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    DLMF defining formula
    Bi ⁡ ( x ) = x 5 / 4 ⁢ e ( 2 / 3 ) ⁢ x 3 / 2 2 5 / 2 ⁢ π ⁢ ⨍ 0 ∞ t - 1 / 2 ⁢ e - ( 2 / 3 ) ⁢ t 3 / 2 ⁢ Ai ⁡ ( t ) x 3 / 2 - t 3 / 2 ⁢ d t Airy-Bi 𝑥 superscript 𝑥 5 4 superscript 𝑒 2 3 superscript 𝑥 3 2 superscript 2 5 2 𝜋 superscript subscript principal-value-integral 0 superscript 𝑡 1 2 superscript 𝑒 2 3 superscript 𝑡 3 2 Airy-Ai 𝑡 superscript 𝑥 3 2 superscript 𝑡 3 2 𝑡 {\displaystyle{\displaystyle\mathrm{Bi}\left(x\right)=\frac{x^{5/4}e^{(2/3)x^{% 3/2}}}{2^{5/2}\pi}\*\pvint_{0}^{\infty}\frac{t^{-1/2}e^{-(2/3)t^{3/2}}\mathrm{% Ai}\left(t\right)}{x^{3/2}-t^{3/2}}\mathrm{d}t}}
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