Fourier series convergence question

  • Thread starter JamesGoh
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  • #1
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Homework Statement



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)


Homework 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)

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
 

Answers and Replies

  • #2
22,089
3,297
Seems ok...
 

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