DLMF:10.22.E70 (Q3444)

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DLMF:10.22.E70
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    Statements

    Defining formula
    ∫ 0 ∞ Y ν ⁡ ( a ⁢ t ) ⁢ J ν + 1 ⁡ ( b ⁢ t ) ⁢ t ⁢ d t t 2 - z 2 = 1 2 ⁢ π ⁢ J ν + 1 ⁡ ( b ⁢ z ) ⁢ H ν ( 1 ) ⁡ ( a ⁢ z ) , superscript subscript 0 Bessel-Y-Weber 𝜈 𝑎 𝑡 Bessel-J 𝜈 1 𝑏 𝑡 𝑡 𝑡 superscript 𝑡 2 superscript 𝑧 2 1 2 𝜋 Bessel-J 𝜈 1 𝑏 𝑧 Hankel-H-1-Bessel-third-kind 𝜈 𝑎 𝑧 {\displaystyle{\displaystyle\int_{0}^{\infty}Y_{\nu}\left(at\right)J_{\nu+1}% \left(bt\right)\frac{t\mathrm{d}t}{t^{2}-z^{2}}=\frac{1}{2}\pi J_{\nu+1}\left(% bz\right){H^{(1)}_{\nu}}\left(az\right),}}
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    DLMF id
    DLMF:10.22.E70
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    constraint
    ℜ ⁡ ν > - 3 2 , ℑ ⁡ z > 0 formulae-sequence 𝜈 3 2 𝑧 0 {\displaystyle{\displaystyle\Re\nu>-\tfrac{3}{2},\Im z>0}}
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