DLMF:10.27.E7 (Q3497)

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DLMF:10.27.E7
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    Statements

    Defining formula
    I ν ⁡ ( z ) = 1 2 ⁢ e ∓ ν ⁢ π ⁢ i / 2 ⁢ ( H ν ( 1 ) ⁡ ( z ⁢ e ± π ⁢ i / 2 ) + H ν ( 2 ) ⁡ ( z ⁢ e ± π ⁢ i / 2 ) ) , modified-Bessel-first-kind 𝜈 𝑧 1 2 superscript 𝑒 minus-or-plus 𝜈 𝜋 𝑖 2 Hankel-H-1-Bessel-third-kind 𝜈 𝑧 superscript 𝑒 plus-or-minus 𝜋 𝑖 2 Hankel-H-2-Bessel-third-kind 𝜈 𝑧 superscript 𝑒 plus-or-minus 𝜋 𝑖 2 {\displaystyle{\displaystyle I_{\nu}\left(z\right)=\tfrac{1}{2}e^{\mp\nu\pi i/% 2}\left({H^{(1)}_{\nu}}\left(ze^{\pm\pi i/2}\right)+{H^{(2)}_{\nu}}\left(ze^{% \pm\pi i/2}\right)\right),}}
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    DLMF id
    DLMF:10.27.E7
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    constraint
    - π ≤ ± ph ⁡ z ≤ 1 2 ⁢ π 𝜋 plus-or-minus phase 𝑧 1 2 𝜋 {\displaystyle{\displaystyle-\pi\leq\pm\operatorname{ph}z\leq\tfrac{1}{2}\pi}}
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