DLMF:13.21.E2 (Q4610)

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DLMF:13.21.E2
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    W κ , μ ( x ) = x Γ ( κ + 1 2 ) ( sin ( κ π - μ π ) J 2 μ ( 2 x κ ) - cos ( κ π - μ π ) Y 2 μ ( 2 x κ ) + env Y 2 μ ( 2 x κ ) O ( κ - 1 2 ) ) , Whittaker-confluent-hypergeometric-W 𝜅 𝜇 𝑥 𝑥 Euler-Gamma 𝜅 1 2 𝜅 𝜋 𝜇 𝜋 Bessel-J 2 𝜇 2 𝑥 𝜅 𝜅 𝜋 𝜇 𝜋 Bessel-Y-Weber 2 𝜇 2 𝑥 𝜅 envelope-Bessel-Y 2 𝜇 2 𝑥 𝜅 Big-O superscript 𝜅 1 2 {\displaystyle{\displaystyle W_{\kappa,\mu}\left(x\right)=\sqrt{x}\Gamma\left(% \kappa+\tfrac{1}{2}\right)\*\left(\sin\left(\kappa\pi-\mu\pi\right)J_{2\mu}% \left(2\sqrt{x\kappa}\right)-\cos\left(\kappa\pi-\mu\pi\right)Y_{2\mu}\left(2% \sqrt{x\kappa}\right)+\mathrm{env}\mskip-2.0mu Y_{2\mu}\left(2\sqrt{x\kappa}% \right)O\left(\kappa^{-\frac{1}{2}}\right)\right),}}
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    DLMF:13.21.E2
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