Plotting a series for n>=1

I have tried plotting the following function but I got a weird plot (really different than expected). I am trying for now to plot the function for a large n (finite). Any help would be great.

the function: f(x)= (1/3) - (8/pi^(2))*{infinite sum from n= 1 of:} [ ( (cos((n*pi)/2) - (2/(n*pi))*sin((n*pi)/2)) /n^(2) ) * cos((n*pi*x)/pi) ]

My code is:

N = 200;

x = linspace(-3*pi, 3*pi, 200);

[X, n] = meshgrid(x, 2:N);

y = (1/3) - (8/pi^(2))*sum((((cos((n*pi)/2)-(2./(n.*pi)).*sin((n*pi)/2))./n.^(2)).*cos((n.*X)/2)),1);

plot(x, y)

Answer 1

[Jos (10584)]

I suggest you avoid meshgrid here. Another tip is to rewrite your function to a somewat simpler form, so you do not loose track of of the opening and closing brackets.

N = 200 ;
n = 1:N % you wrote 2:N in your code??
m = (1:N)*(pi/2) ; % simpler form
sumfun = @(x) sum((cos(m) - (1./m).*sin(m)./ (n.^2) ) .* cos(n.*x))
x = linspace(-3*pi, 3*pi, 200);
y = (1/3) - (8/(pi^2)) * arrayfun(@(z) sumfun(z), x) ; % apply to each value of x
plot(x,y,'b.-')

[Sultan Al-Hammadi]

there might be something wrong with you code as it should look like a periodic function: equals 1-x^2 from -1 to 1 and equals zero from (-2 to -1) & (1 to 2).