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.