(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

f(x) = 5, -pi <= x <= 0

f(x) = 3, 0 < x <= pi

f(x) is the function of interest

Find the x-points where F(x) fails to converge

to f(x)

2. Relevant equations

F(x) = f(x) if f is continuous at [itex]x\in(-L,L)[/itex]

F(x) = 0.5[ f(x-) + f(x+) ] if f is discontinous at [itex]x\in(-L,L)[/itex]

F(x) is the fourier series of f(x)

3. The attempt at a solution

Would the Fourier series, F(x) fail to converge

at +pi and -pi ?

My reasoning is as follows

- At both -pi and +pi, we have the start and end value of f(x)

- By definition F(x) = (1/2)f(x-) + (1/2)f(x+)

- Lets take x = -pi, which means f(x) =5 and f(-x) = 3

- F(-pi) = (1/2)(5) + (1/2)(3) = 8/2 = 4 which is not equal to f(-pi)=5

- From the latter, we can conclude that F(-pi) fails to converge to

the value given from f(-pi) since their not equal to each other

Just want to check if my reasoning is ok since no answer was provided to this question

thanks

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# Fourier series convergence question

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