Does anyone know how to code this summation equation that includes exponential and sine function?

result = compute_summation(1,100); % Computes the series for x = 1 with 100 terms
disp(result);
   20.4225
function total = compute_summation(x, num_terms)
    if nargin < 2
        num_terms = 100; % Default number of terms
    end
    total = 0;
    for m = 1:num_terms
        exponential_part = exp(-(2*m)^2 * pi^2 / 900);
        sine_part = sin(2 * m * pi / 30);
        term = (180 / (2 * m * pi)) * exponential_part * sine_part;
        total = total + term;
    end
end

Note

Please note that computing an actual infinite series may not be possible due to computational limits, so you would typically compute a partial sum or find a closed-form if it exists.

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Dyuman Joshi 2024-1-6

The series has an infinite summation, so the for loop will take too long for big values of num_terms (~1e9/1e10), nor will it give accurate results for bigger values of x.

And the exponential term is incorrect, as it is missing pi^2.

Hassaan 2024-1-6

编辑：Hassaan 2024-1-6

在 MATLAB Online 中打开

@Dyuman Joshi Thanks for pointing out I have corrected the exponential term. Also, I am not sure if MATLAB can do infinite series obviously not numerically nor symbolically dont we have to trancuate at some point?. Also I tried the syms approach.

syms m t;

% Define the general term of the series

general_term = (180/(2*m*pi)) * exp(-(2*m)^2 * pi^2 *t / 900) * sin(2*m*pi/30);

% Compute the summation

% Note: MATLAB might not be able to resolve this symbolically for an infinite series

% So we use a large number for the upper limit, say 100 terms

N = 100; % you can set N to a different value to approximate the infinite sum or inf

total_sum = symsum(general_term, m, 1, N);

% Display the symbolic sum

disp(total_sum);