DLMF:10.27.E11 (Q3501)

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DLMF:10.27.E11
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    Statements

    test
    Y ν ⁡ ( z ) = e ± ( ν + 1 ) ⁢ π ⁢ i / 2 ⁢ I ν ⁡ ( z ⁢ e ∓ π ⁢ i / 2 ) - ( 2 / π ) ⁢ e ∓ ν ⁢ π ⁢ i / 2 ⁢ K ν ⁡ ( z ⁢ e ∓ π ⁢ i / 2 ) , Bessel-Y-Weber 𝜈 𝑧 superscript 𝑒 plus-or-minus 𝜈 1 𝜋 𝑖 2 modified-Bessel-first-kind 𝜈 𝑧 superscript 𝑒 minus-or-plus 𝜋 𝑖 2 2 𝜋 superscript 𝑒 minus-or-plus 𝜈 𝜋 𝑖 2 modified-Bessel-second-kind 𝜈 𝑧 superscript 𝑒 minus-or-plus 𝜋 𝑖 2 {\displaystyle{\displaystyle Y_{\nu}\left(z\right)=e^{\pm(\nu+1)\pi i/2}I_{\nu% }\left(ze^{\mp\pi i/2}\right)-(2/\pi)e^{\mp\nu\pi i/2}K_{\nu}\left(ze^{\mp\pi i% /2}\right),}}
    0 references
    DLMF id
    DLMF:10.27.E11
    0 references
    constraint
    - 1 2 ⁢ π ≤ ± ph ⁡ z ≤ π 1 2 𝜋 plus-or-minus phase 𝑧 𝜋 {\displaystyle{\displaystyle-\tfrac{1}{2}\pi\leq\pm\operatorname{ph}z\leq\pi}}
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    Symbols used
    Bessel function of the second kind
    test
    Y ν ⁡ ( z ) Bessel-Y-Weber 𝜈 𝑧 {\displaystyle{\displaystyle Y_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E3.m2aadec
    0 references
     
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