Plotting a summation as a function of two variables

Hello, Sorry I'm new to matlab and I couldn't work out the solution to this question with the help.

I'm plotting a function of \theta and \phi as a density plot over the surface of the sphere.

For an easy function f, I had luck using the following code:

res = 50;
lambda = linspace(-pi,pi,res);
theta = linspace(-pi/2,pi/2,ceil(res/2));
[L,T] = meshgrid(lambda,theta);
n=10;
f=(n.*(cos((T-pi/2)/2)).^2+1).*exp(-n.*(sin((T-pi/2)/2).^2));
[X,Y,Z] = sph2cart(L,T,1);
clf;
surf(X,Y,Z,f);

Now I'm trying to do the same but with a more difficult function you can see here

with \mu \nu numbers... We can use a simpler function as a minimal example, like

\sum_{S=0}^{1000} (2S+1) (cos(\theta/2))^2

How can I do to represent this function (of \theta and \phi)over the sphere just like I did with the example below?

Many Thanks

[Fatma Abdullah]

do you have any values for mue, v, and N ?!