Question

Find the real Fourier series of the piece-wise defined function

f(x) = Pi+x -2<=x<2

Answer #1

Find the Fourier series of the function:
f(x) =
{0, -pi < x < 0
{1, 0 <= x < pi

f(t) is defined on (-pi,pi] as
t^3 Extend periodically and compute the fourier series.

Calculate the Fourier Series S(x) of f(x) = sin(x/2), -pi < x
< pi. What is S(pi) = ?

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

Expand in Fourier Series.
f(x) = (sinx)^3, -pi < x < pi

Find the Fourier series of the function f(x) = |x|, −π/2 < x
< π/2 , with period π.

Find the Taylor series for the function f(x)=sin(pi(x)-pi/2)
with center a=1

find the Fourier series to represent the function
f(x)=x-x^2 where x{-π,π}

Derive the Fourier series for the function f(x) = x + 1/2 for −1
< x < 1; plot the function and its Fourier series for −3 <
x < 3.

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?

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