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Can someone help me solve the following integral

[tex]

\int_0^{2\pi} exp[-i(G_x \cos\theta + G_y \sin\theta] d\theta

[/tex]

I've tried splitting the exponential into a product of two exponetials and rewriting the exponentials in terms of sines and cosines. But I always end up getting stuck. Some of my rewritings ended up looking close to a Bessel function but it's just not quite the same. Can someone just give me a hint on where to start?

Im not sure about the limits, they might have to be from [tex]-\pi[/tex] to [tex]\pi[/tex] but I don't believe that should change anything.

Thanks in advance

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# Integral of exponential involving sines and cosines

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