DLMF:13.21.E24 (Q4632)

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DLMF:13.21.E24
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    W - κ , μ ( x e - π i ) = e ( κ - 1 6 ) π i c ^ ( κ , μ ) Ψ ^ ( κ , μ , x ) ( Ai ( κ 2 3 ζ ^ e - 2 3 π i ) + envBi ( κ 2 3 ζ ^ ) O ( κ - 1 ) ) , Whittaker-confluent-hypergeometric-W 𝜅 𝜇 𝑥 superscript 𝑒 𝜋 imaginary-unit superscript 𝑒 𝜅 1 6 𝜋 imaginary-unit ^ 𝑐 𝜅 𝜇 ^ Ψ 𝜅 𝜇 𝑥 Airy-Ai superscript 𝜅 2 3 ^ 𝜁 superscript 𝑒 2 3 𝜋 imaginary-unit envelope-Airy-Bi superscript 𝜅 2 3 ^ 𝜁 Big-O superscript 𝜅 1 {\displaystyle{\displaystyle W_{-\kappa,\mu}\left(xe^{-\pi\mathrm{i}}\right)=e% ^{(\kappa-\frac{1}{6})\pi\mathrm{i}}\widehat{c}(\kappa,\mu)\widehat{\Psi}(% \kappa,\mu,x)\left(\mathrm{Ai}\left(\kappa^{\frac{2}{3}}\widehat{\zeta}e^{-% \frac{2}{3}\pi\mathrm{i}}\right)+\mathrm{envBi}\left(\kappa^{\frac{2}{3}}% \widehat{\zeta}\right)O\left(\kappa^{-1}\right)\right),}}
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    DLMF:13.21.E24
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