Finding the Fourier Series

1. Find the Fourier sine series of f(x)=1, 0the initial condition f(0,x)=1 if |x|L/2 Please see the attachment to view the questions with correct mathematical notation (and also phrased slightly differe

Suppose f(t) and g(t) are 2π periodic functions with Fourier series representations {see attachment}. Find the Fourier series of {see attachment}.

We use the Fourier expansions of certain poynomial functions to compute the sum of some useful numerical series. The formulas are quite general and give, at the end, the Fourier expansion of every polynomial function. By the way, these formulas can be also used for a numerical approximation of pi=3.14....

Determine the Fourier series for the function: f(t) = (0, for -2 â?¤ t <0 (t, for 0 â?¤ t <2

Please see the attached file for the fully formatted problem. Let Y: R --> R be the periodic function whose restriction to [0,1] is X (0,1/2) - X(1/2,1) Y is an odd function. S 1--> 0 Y(x) cos 2pi kx dx = S 1/2-->-1/2 Y(x) cos 2pi kx dx Vk Conclude the the complex Fourier Series...can be expressed in the form...

Please work through attached problem and let me know how you did it. Thank you.

Find the complex Fourier series coefficients for the function x(t) depicted in the below figure Please see

Please help ... what is the Fourier series expansion of f(t). It is a multiple answer question. (See attached file for full problem description)

There is an attached file with further information regarding the problem. Find by inspection the first seven Fourier coefficients {a0, a1, b1, a2, b2, a3, b3} of the function: f(x) = 14-cos(Pi*x/10) + 3sin(Pi*x/10) + 0.5cos(Pi*x/5) + 5sin(3*Pi*x/10)