DLMF:36.13.E8 (Q10017)

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DLMF:36.13.E8
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    z ( ρ , ϕ ) = 2 π ( ρ - 1 / 3 u ( ϕ ) cos ( ρ f ~ ( ϕ ) ) Ai ( - ρ 2 / 3 Δ ( ϕ ) ) ( 1 + O ( 1 / ρ ) ) + ρ - 2 / 3 v ( ϕ ) sin ( ρ f ~ ( ϕ ) ) Ai ( - ρ 2 / 3 Δ ( ϕ ) ) ( 1 + O ( 1 / ρ ) ) ) , 𝑧 𝜌 italic-ϕ 2 𝜋 superscript 𝜌 1 3 𝑢 italic-ϕ 𝜌 ~ 𝑓 italic-ϕ Airy-Ai superscript 𝜌 2 3 Δ italic-ϕ 1 Big-O 1 𝜌 superscript 𝜌 2 3 𝑣 italic-ϕ 𝜌 ~ 𝑓 italic-ϕ diffop Airy-Ai 1 superscript 𝜌 2 3 Δ italic-ϕ 1 Big-O 1 𝜌 {\displaystyle{\displaystyle z(\rho,\phi)=2\pi\left(\rho^{-1/3}u(\phi)\cos% \left(\rho\widetilde{f}(\phi)\right)\mathrm{Ai}\left(-\rho^{2/3}\Delta(\phi)% \right)\*(1+O\left(1/\rho\right))+\rho^{-2/3}v(\phi)\sin\left(\rho\widetilde{f% }(\phi)\right)\mathrm{Ai}'\left(-\rho^{2/3}\Delta(\phi)\right)\*(1+O\left(1/% \rho\right))\right),}}
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    DLMF:36.13.E8
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