DLMF:10.4.E7 (Q3022)

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DLMF:10.4.E7
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    Statements

    test
    H ν ( 1 ) ⁡ ( z ) = i ⁢ csc ⁡ ( ν ⁢ π ) ⁢ ( e - ν ⁢ π ⁢ i ⁢ J ν ⁡ ( z ) - J - ν ⁡ ( z ) ) = csc ⁡ ( ν ⁢ π ) ⁢ ( Y - ν ⁡ ( z ) - e - ν ⁢ π ⁢ i ⁢ Y ν ⁡ ( z ) ) , Hankel-H-1-Bessel-third-kind 𝜈 𝑧 𝑖 𝜈 𝜋 superscript 𝑒 𝜈 𝜋 𝑖 Bessel-J 𝜈 𝑧 Bessel-J 𝜈 𝑧 𝜈 𝜋 Bessel-Y-Weber 𝜈 𝑧 superscript 𝑒 𝜈 𝜋 𝑖 Bessel-Y-Weber 𝜈 𝑧 {\displaystyle{\displaystyle{H^{(1)}_{\nu}}\left(z\right)=i\csc\left(\nu\pi% \right)\left(e^{-\nu\pi i}J_{\nu}\left(z\right)-J_{-\nu}\left(z\right)\right)=% \csc\left(\nu\pi\right)\left(Y_{-\nu}\left(z\right)-e^{-\nu\pi i}Y_{\nu}\left(% z\right)\right),}}
    0 references
    DLMF id
    DLMF:10.4.E7
    0 references
    Symbols used
    Bessel function of the first kind
    test
    J ν ⁡ ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E2.m2addec
    0 references
    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.m2addec
    0 references
     
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