MHB Calculating Fourier Co-Efficent An of an Even Square Function

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The discussion revolves around calculating the Fourier coefficient An for an even square function. The original poster struggled with the problem but ultimately concluded that their answer, 4sin(npi/2)/npi, was correct, contradicting the teacher's provided answer of -4/npi. They expressed appreciation for any help but later confirmed their solution was accurate. The thread highlights the importance of verifying answers in mathematical problems. The resolution underscores the complexity of Fourier series calculations and the potential for discrepancies in educational settings.
Metalsie
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Nevermind guys, it appears that my answer is correct.
 
Metalsie said:
Nevermind guys, it appears that my answer is correct.

Your follow-up post to let us know what you found is greatly appreciated. (Yes)
 
The answer provided by the teacher (-4/npi) was basically wrong and mine was right. Sorry.

Here is the "same" problem solved

Calculating Fourier Series 1
 

Thread 'Proving that convexity implies second order derivative being positive'

There are probably loads of proofs of this online, but I do not want to cheat. Here is my attempt: Convexity says that $$f(\lambda a + (1-\lambda)b) \leq \lambda f(a) + (1-\lambda) f(b)$$ $$f(b + \lambda(a-b)) \leq f(b) + \lambda (f(a) - f(b))$$ We know from the intermediate value theorem that there exists a ##c \in (b,a)## such that $$\frac{f(a) - f(b)}{a-b} = f'(c).$$ Hence $$f(b + \lambda(a-b)) \leq f(b) + \lambda (a - b) f'(c))$$ $$\frac{f(b + \lambda(a-b)) - f(b)}{\lambda(a-b)}...
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