Verifying Fourier Series In MATLAB

[Jovany_17]

HI please help me this could someone verify it for me please find attachement

clc;
clear all;
k=0;
s=0;
N=inf;
for i=1:N
s=s+(1/(k^2+1));
k=k+1;
end

syms x n
a0=1/pi*int(cosh(x),-pi,pi);
an=1/pi*int(cosh(x)*cos(n*x),-pi,pi);
bn=1/pi*int(cosh(x)*sin(n*x),-pi,pi);

fs=0;

for l=0:100
fs=fs+(an*cos(l*x)+bn*sin(l*x))
end

fs-fs+a0/2;

 

[mathman]

HI please help me this could someone verify it for me please find attachement

clc;
clear all;
k=0;
s=0;
N=inf;
for i=1:N
s=s+(1/(k^2+1));
k=k+1;
end

syms x n
a0=1/pi*int(cosh(x),-pi,pi);
an=1/pi*int(cosh(x)*cos(n*x),-pi,pi);
bn=1/pi*int(cosh(x)*sin(n*x),-pi,pi);

fs=0;

for l=0:100
fs=fs+(an*cos(l*x)+bn*sin(l*x))
end

fs-fs+a0/2;

The calculation of s looks OK. It could have been done slightly easier.
N=inf;
s=1;
for k = 1:N
s=s+(1/(k^2+1));
end
The Fourier series sum has a couple of errors. I would do the following:
fs = a0/2;
N = inf;
for n = 1:N
fs=fs+(an*cos(n*x)+bn*sin(n*x));
end

 

[Jovany_17]

Thanks

 

[mathman]

A further simplification: Except for a0, the values of an and bn can be calculated inside the loop, so they don't have to be stored in advance.

 

[alphy]

The code provided appears to be verifying the Fourier series for the function cosh(x) in MATLAB. It calculates the coefficients a0, an, and bn using symbolic integration and then uses a for loop to calculate the series up to a certain number of terms (in this case, 100). Finally, it verifies the series by subtracting it from itself and adding the constant term a0/2. This code seems to be a valid way of verifying the Fourier series, but it would be helpful to include comments and a clear explanation of the code for better understanding. Additionally, it would be beneficial to include a plot of the original function and the Fourier series approximation for visual verification.