Problems about Fourier expansion?

kring_c14
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Homework Statement



just wondering if anyone knew a website that has solved problems about Fourier expansion??

all i can find are notes and discussions about it..

a gazallion thanks everyone

Homework Equations





The Attempt at a Solution

 
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Is Fourier series and Fourier expansion just the same?
 
The problem is that to solve Fourier expansion problems you just have to be able to integrate... nothing more. So if you can't do a problem, practise your integration! A Fourier series is what you get when you perform a Fourier expansion.
 
ahhh.. now i understand.. thank you..
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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