DLMF:10.27.E9 (Q3499)

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DLMF:10.27.E9
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    π i J ν ( z ) = e - ν π i / 2 K ν ( z e - π i / 2 ) - e ν π i / 2 K ν ( z e π i / 2 ) , 𝜋 𝑖 Bessel-J 𝜈 𝑧 superscript 𝑒 𝜈 𝜋 𝑖 2 modified-Bessel-second-kind 𝜈 𝑧 superscript 𝑒 𝜋 𝑖 2 superscript 𝑒 𝜈 𝜋 𝑖 2 modified-Bessel-second-kind 𝜈 𝑧 superscript 𝑒 𝜋 𝑖 2 {\displaystyle{\displaystyle\pi iJ_{\nu}\left(z\right)=e^{-\nu\pi i/2}K_{\nu}% \left(ze^{-\pi i/2}\right)-e^{\nu\pi i/2}K_{\nu}\left(ze^{\pi i/2}\right),}}
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    DLMF:10.27.E9
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    | ph z | 1 2 π phase 𝑧 1 2 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\tfrac{1}{2}\pi}}
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