How can I use symsum function to calculate this equation?

As the file i attach, i want to caculate the equation.

The boundary typed on picture is wrong.

The correction is n=0 to n=1000.

And J-function is bessel function.

H-function is hankel funtion.

Beta*alpha=1.2*pi.

epsilon n=1 when n=0.

epsilon n=2 when n is not equal to 0.

Answer 1

[Rohit Pappu]

%% Define constants
syms n phi lambda;
beta_alpha = 1.2*pi;

epsilon0 = 1; %% Epsilon when n=0
epsilon = 2; %% Epsilon when n~=0

%% Define equation for n = 1 to 100
f = epsilon*besselj(n,beta_alpha)*cos(n*phi)/besselh(n,2,beta_alpha);

%% Use symsum to find sum of series , f/2 case is when n = 0
sum = (2*pi/lambda)*(abs(symsum(f,n,[1,100])+symsum(f/2,n,[0,0]))^2);

[Walter Roberson]

Why symsum 0 to 0? Why not just use subs(f/2,n,0) ?

[Rohit Pappu]

Edit : subs can be used to denote the n=0 term

%% Use symsum to find sum of series , f/2 case is when n = 0
sum = (2*pi/lambda)*(abs(symsum(f,n,[1,100])+subs(f/2,n,0))^2);