DLMF:9.6.E25 (Q2805)

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DLMF:9.6.E25
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    Bi ( z ) = 1 3 1 / 6 Γ ( 2 3 ) e - ζ F 1 1 ( 1 6 ; 1 3 ; 2 ζ ) + 3 5 / 6 2 2 / 3 Γ ( 1 3 ) ζ 2 / 3 e - ζ F 1 1 ( 5 6 ; 5 3 ; 2 ζ ) , Airy-Bi 𝑧 1 superscript 3 1 6 Euler-Gamma 2 3 superscript 𝑒 𝜁 Kummer-confluent-hypergeometric-M-as-1F1 1 6 1 3 2 𝜁 superscript 3 5 6 superscript 2 2 3 Euler-Gamma 1 3 superscript 𝜁 2 3 superscript 𝑒 𝜁 Kummer-confluent-hypergeometric-M-as-1F1 5 6 5 3 2 𝜁 {\displaystyle{\displaystyle\mathrm{Bi}\left(z\right)=\frac{1}{3^{1/6}\Gamma% \left(\tfrac{2}{3}\right)}e^{-\zeta}{{}_{1}F_{1}}\left(\tfrac{1}{6};\tfrac{1}{% 3};2\zeta\right)+\frac{3^{5/6}}{2^{2/3}\Gamma\left(\tfrac{1}{3}\right)}\zeta^{% 2/3}e^{-\zeta}{{}_{1}F_{1}}\left(\tfrac{5}{6};\tfrac{5}{3};2\zeta\right),}}
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    DLMF:9.6.E25
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