# How can I use symsum function to calculate this equation?

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zheng-ning zhu on 21 Dec 2020
Commented: Rohit Pappu on 28 Dec 2020
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.

Rohit Pappu on 28 Dec 2020
%% 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);
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Rohit Pappu on 28 Dec 2020
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);