Question

Find the Fourier series of the function:

f(x) =

{0, -pi < x < 0

{1, 0 <= x < pi

Answer #1

fourier expansion, piecewise function.
f(x){ pi , -1<x<0
-pi , 0<x<1

Find the Fourier series of the function f on the given
interval.
f(x) =
0,
−π < x < 0
1,
0 ≤ x < π

Find the real Fourier series of the piece-wise defined
function
f(x) = Pi+x -2<=x<2

Expand the Fourier Series.
f(x) = 1- x, -pi < x < pi

a. Let f be an odd function. Find the Fourier series of f on
[-1, 1]
b. Let f be an even function. Find the Fourier series of f on
[-1, 1].
c. At what condition for f would make the series converge to f
at x=0 and x=1?

Find the fourier series representation of each periodic
function
f(x) = 0, -4 <x<0
f(x) = 8, 0<=x<=1
f(x) = 0, 1<x<4

Find a Fourier Series expansion for the function f(x)= xcos(3x)
on the domain from x = [-pi,pi]

Find the Fourier series for the following function (which has
period 2): f(x)= −x if −1<x<0
x if 0 < x < 1

Find the half-range cosine Fourier series expansion of the
function f(x) = x + 3;
0 < x < 1.

Compute the complex Fourier series of the function f(x)= 0 if −
π < x < 0, 1 if 0 ≤ x < π
on the interval [−π, π]. To what value does the complex Fourier
series converge at x = 0?

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