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Justify an equality involving hyperbolic cosine and Fourier series
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[QUOTE="brmath, post: 4516103, member: 486151"] Here's a thought. Are you familiar with breaking up a fraction like ##\frac{A + B} {C + D}##? Just say ## \frac {x}{C} + \frac {y}{D}## = ##\frac{A + B} {C + D}##. On the left side, add up the two fractions as you did in elementary school and solve for x and y. If you do that to your integrand, you will wind up with the sum of two exponentials, and I think you can just integrate it. Whether that trick gets you to the right series I don't know, but it's worth a shot. I'm also a little worried about your summations -- when you multiply through by i don't you get a -x in the numerator? Finally -- are you sure this is a Fourier series problem? Is it in that chapter of some book? I am not above expanding cotx in a Taylor's series and seeing if that can be kicked around to get what you need. [/QUOTE]
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Justify an equality involving hyperbolic cosine and Fourier series
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