Hi, I need help on the following problem on Fourier series:(adsbygoogle = window.adsbygoogle || []).push({});

Let phi(x)=1 for 0<x<pi. Expand

[tex] 1 = \sum\limits_{n = 0}^\infty B_n cos[(n+ \frac{1}{2})x] [/tex]

a) Find B_n.

b) Let -2pi < x < 2pi. For which such x does this series converge? For each such x, what is the sum of the series?

c) Apply Parseval's equality to this series. Use it to calculate the sum

1 + 1/(3^2) + 1/(5^2) + 1/(7^2) + ....

I know the formula for B_n for a function's Fourier series on the interval -L < x < L, so in this question I need to do some kind of odd or even extension for parts a and b, but I don't know how. Please help. Thanks.

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# Fourier series problem

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