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Prove that \[ J_{n}(x)=\frac{1}{\sqrt{\pi} \sqrt{n}}\left(\frac{x}{2}\right)^{n} \int_{0}^{\pi} \cos (x \sin \phi) \cos ^{2 n} \phi d \phi \]

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Prove that \[ J_{n}(x)=\frac{1}{\sqrt{\pi} \sqrt{n}}\left(\frac{x}{2}\right)^{n} \int_{0}^{\pi} \cos (x \sin \phi) \cos ^{2 n} \phi d \phi \]
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