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This result is used to define the function c(n) as follows:
DEFINE(‘c(n) = - (((-1)^n-1)/(n^2*π^2*(-1)^n)’)
i.e.,
Next, we define function F(X,k,c0) to calculate the Fourier series (if you
completed example 1, you already have this function stored):
DEFINE(‘F(X,k,c0) = c0+Σ(n=1,k,c(n)*EXP(2*i*π*n*X/T)+
c(-n)*EXP(-(2*i*π*n*X/T))’),
To compare the original function and the Fourier series we can produce the
simultaneous plot of both functions. The details are similar to those of example
1, except that here we use a horizontal range of 0 to 2 and a vertical range
from 0 to 1, and adjust the equations to plot as shown here:
The resulting graph is shown below for k = 5 (the number of elements in the
series is 2k+1, i.e., 11, in this case):
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