DLMF:9.6.E4 (Q2784)

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DLMF:9.6.E4
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    Bi ( z ) = z / 3 ( I 1 / 3 ( ζ ) + I - 1 / 3 ( ζ ) ) = 1 2 z / 3 ( e π i / 6 H 1 / 3 ( 1 ) ( ζ e - π i / 2 ) + e - π i / 6 H 1 / 3 ( 2 ) ( ζ e π i / 2 ) ) = 1 2 z / 3 ( e - π i / 6 H - 1 / 3 ( 1 ) ( ζ e - π i / 2 ) + e π i / 6 H - 1 / 3 ( 2 ) ( ζ e π i / 2 ) ) , Airy-Bi 𝑧 𝑧 3 modified-Bessel-first-kind 1 3 𝜁 modified-Bessel-first-kind 1 3 𝜁 1 2 𝑧 3 superscript 𝑒 𝜋 𝑖 6 Hankel-H-1-Bessel-third-kind 1 3 𝜁 superscript 𝑒 𝜋 𝑖 2 superscript 𝑒 𝜋 𝑖 6 Hankel-H-2-Bessel-third-kind 1 3 𝜁 superscript 𝑒 𝜋 𝑖 2 1 2 𝑧 3 superscript 𝑒 𝜋 𝑖 6 Hankel-H-1-Bessel-third-kind 1 3 𝜁 superscript 𝑒 𝜋 𝑖 2 superscript 𝑒 𝜋 𝑖 6 Hankel-H-2-Bessel-third-kind 1 3 𝜁 superscript 𝑒 𝜋 𝑖 2 {\displaystyle{\displaystyle\mathrm{Bi}\left(z\right)=\sqrt{z/3}\left(I_{1/3}% \left(\zeta\right)+I_{-1/3}\left(\zeta\right)\right)=\tfrac{1}{2}\sqrt{z/3}% \left(e^{\pi i/6}{H^{(1)}_{1/3}}\left(\zeta e^{-\pi i/2}\right)+e^{-\pi i/6}{H% ^{(2)}_{1/3}}\left(\zeta e^{\pi i/2}\right)\right)=\tfrac{1}{2}\sqrt{z/3}\left% (e^{-\pi i/6}{H^{(1)}_{-1/3}}\left(\zeta e^{-\pi i/2}\right)+e^{\pi i/6}{H^{(2% )}_{-1/3}}\left(\zeta e^{\pi i/2}\right)\right),}}
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    DLMF:9.6.E4
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