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Prove the following identity:

\begin{equation} e^{ia\sin{x}}=\sum_{-\infty}^{+\infty}J_k(a) e^{ikx}, \end{equation}

where $a$ is a real constant and $J_k$ is the Bessel function of the first type of order $k$.

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    This was already bumped by Community, so I took the opportunity to make anotherwise way too minor a correction and upvoted vesszabo'z solution along the way :-)2013-09-15

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