How can I express this very long summation in Matlab? I'm having trouble

I'm looking to plot the velocity contours of a fluid flow over a cross section (part e). I already have the two variables (eta and zeta) and I also know their bounds so I was able to succesfully setup the meshgrid. Now I just need to write my function but I am blanking out hard. Is there an easy way to express everything to the right of the summation in Matlab? Also, the summation does not have to go from 0 to infinity, my teacher said it's fine to evaluate just the first 5 terms. I would really appreicate any input.

[Jason Lee]

I've tried using a for loop but I was getting an error because my summation starts at 0 which is not allowed

[KSSV]

Show us your code which gives error....we can help you to correct you that.

[Jason Lee]

[z,n]=meshgrid(-0.5:0.005:0.5,-1:0.005:1);
w = 0;
for i = 0:5
    w = w + (((-1).^i)/(3*i + 1).^3) .* ((cosh((2*i + 1) .* pi .* z))./(cosh((2*i + 1) .* pi))) .* cos((2*i + 1).* (pi/2) .* n);
end
Velocity = 1 - n.^2 -1.03 .* w
axis on
contour(z, n, Velocity);

Here's what I have so far. My problem is definitely in the loop somewhere but I'm just blanking out on how to fix it

[Walter Roberson]

A for loop starting from 0 is not a problem.

If you need to use the for loop value as an index, add 1 to it to get the index.

Answer 1

[David Hill]

I believe that below should work for you. I did not try it out since you did not provide all the information, but you have to compute the calculation for each (eta,zeta) pair in the meshgrid.

m=0:10;
[eta,zeta]=meshgrid()
for k=1:size(eta,1)
w(k,:)=arrayfun(@(et,ze)K*b^2/2*(1-et^2-4*(2/pi)^3*sum((-1).^m.*cosh((2*m+1)*pi*a*ze/2/b).*...
    cos((2*m+1)*pi*et/2)./((2*m+1).^3.*cosh((2*m+1)*pi*a/2/b)))),eta(k,:),zeta(k,:));
end

[Jason Lee]

Thank you for your input. I tried that for my meshgrid values but wasn't able to get it, I'll let you know if I get it. Appreciate the help

[David Hill]

It works and runs for me. I did not know what the constants were, so I set them to 1.

m=0:10;
[eta,zeta]=meshgrid(-0.5:0.005:0.5,-1:0.005:1);
K=1;
b=1;
a=1;
w=zeros(size(eta));
for k=1:size(eta,1)
w(k,:)=arrayfun(@(et,ze)K*b^2/2*(1-et^2-4*(2/pi)^3*sum((-1).^m.*cosh((2*m+1)*pi*a*ze/2/b).*...
    cos((2*m+1)*pi*et/2)./((2*m+1).^3.*cosh((2*m+1)*pi*a/2/b)))),eta(k,:),zeta(k,:));
end

[Jason Lee]

That's exactly what I was looking for actually. Thank you so much! I think I just accidently forgot to copy something when I copied and pasted it in my screen.