Indexing definite Summation notation

I want to input the formula below into MATLAB to ultimately commpute 'W':

Can you please tell me if how can I correct my code or suggest a more concise one?

syms i

for i = 1:m

i = i + 1;

phi(i) = atan((d1+(i*d2/(m+1)))/(R/(3*m+3)));

W = symsum(sin(gama + ((pi/2) - (phi*i))), i, 1, m);

end

Answer 1

[Ameer Hamza]

This numerically estimate the summation

d1 = 0.1; % example values
d2 = 0.5;
R = 1;

phi_i = @(ii, m) atan((d1 + (ii*d2)./(m+1))./(R/(3*(m+1))));
W = @(m, delta) sum(sin(delta + pi/2 - phi_i(1:m, m)));

W(10, 2)

[Jay]

I have to add a new variable beta_i to the original equation, where beta = 2 x phi.

Beta is also indexed: I did B_i = 2*phi_i

Can you please tell me how can I multiplly phi_i directly by a scalar to get the betas?

phi_i = @(ii, m) atan((d1 + (ii*d2)./(m+1))./(R/(3*(m+1))));

H = @(m) cos(gama) + sum(cos(gama + (pi/2 - phi_i))) +...

omega *sin(B(m)).