DLMF:10.9.E20 (Q3089)

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DLMF:10.9.E20
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    J ν ( z ) = Γ ( 1 2 - ν ) ( 1 2 z ) ν π 3 2 i 0 ( 1 + ) cos ( z t ) ( t 2 - 1 ) ν - 1 2 d t , Bessel-J 𝜈 𝑧 Euler-Gamma 1 2 𝜈 superscript 1 2 𝑧 𝜈 superscript 𝜋 3 2 𝑖 superscript subscript 0 limit-from 1 𝑧 𝑡 superscript superscript 𝑡 2 1 𝜈 1 2 𝑡 {\displaystyle{\displaystyle J_{\nu}\left(z\right)=\frac{\Gamma\left(\frac{1}{% 2}-\nu\right)(\frac{1}{2}z)^{\nu}}{\pi^{\frac{3}{2}}i}\int_{0}^{(1+)}\cos\left% (zt\right)(t^{2}-1)^{\nu-\frac{1}{2}}\mathrm{d}t,}}
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    DLMF:10.9.E20
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    ν 1 2 , 3 2 , 𝜈 1 2 3 2 {\displaystyle{\displaystyle\nu\neq\tfrac{1}{2},\tfrac{3}{2},\ldots}}
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