DLMF:10.9#Ex3 (Q3075)

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DLMF:10.9#Ex3
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    J 0 ( x ) = 2 π 0 sin ( x cosh t ) d t , Bessel-J 0 𝑥 2 𝜋 superscript subscript 0 𝑥 𝑡 𝑡 {\displaystyle{\displaystyle J_{0}\left(x\right)=\frac{2}{\pi}\int_{0}^{\infty% }\sin\left(x\cosh t\right)\mathrm{d}t,}}
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