DLMF:10.9#Ex1 (Q3073)

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DLMF:10.9#Ex1
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    J ν ⁡ ( x ) = 2 π ⁢ ∫ 0 ∞ sin ⁡ ( x ⁢ cosh ⁡ t - 1 2 ⁢ ν ⁢ π ) ⁢ cosh ⁡ ( ν ⁢ t ) ⁢ d t , Bessel-J 𝜈 𝑥 2 𝜋 superscript subscript 0 𝑥 𝑡 1 2 𝜈 𝜋 𝜈 𝑡 𝑡 {\displaystyle{\displaystyle J_{\nu}\left(x\right)=\frac{2}{\pi}\int_{0}^{% \infty}\sin\left(x\cosh t-\tfrac{1}{2}\nu\pi\right)\cosh\left(\nu t\right)% \mathrm{d}t,}}
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    DLMF:10.9#Ex1
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