Fourier series doesn't approximate with bigger number of points

Hello.

I am trying to approximate a function using fourier series, but using a larger input of points N I get an aproximation bigger than the original graph. I can't seem to find where the problem is any help is appreciated. First plot is the function, then it's the fourier series versus precise graph and then An and Bn koeficient correlation from N.

code:

clc
clear
%conditions
T=3;
h=0.1;
a=-3;
b=3;
N=36;
x=a:h:b;
n1=0;
%original function
for iks=a:h:b
    n1=n1+1;
    graf1(1,n1)=iks;
    graf1(2,n1)=funk(iks);
end
%plot
plot(graf1(1,:),graf1(2,:));
ylabel('y')
xlabel('x')

%Fourier series and aproximation
A0=0;
for iks2=0:h:T
    A0=A0+funk(iks2);
end
A0=A0.*2.*h./T;

AnBn=zeros(3,N);
for nr=1:N
    for n2=-T:h:T
        AnBn(1,nr)=AnBn(1,nr)+funk(n2)*cos(2*nr*pi*n2/T);
        AnBn(2,nr)=AnBn(2,nr)+funk(n2)*sin(2*nr*pi*n2/T);
    end
end
AnBn=AnBn.*h./T;

n3=0;
aprox1=zeros(2,(b-a)./h);
for iks3=a:h:b
    aprox=0;
    for k=1:N
        aprox=aprox+(AnBn(1,k).*cos(2*k*pi*iks3/T)+AnBn(2,k).*sin(2*k*pi*iks3/T));
    end
    aprox=aprox+A0/2;
    n3=n3+1;
    aprox1(1,n3)=iks3;
    aprox1(2,n3)=aprox;
end
%ploting
figure
plot(aprox1(1,:),aprox1(2,:),'b',graf1(1,:),graf1(2,:),'r');

ylabel('y')
xlabel('x')
legend('Aproksimated f','Original f')

for nr1=1:N
    AnBn(3,nr1)=nr1;
end

figure
scatter(AnBn(3,:),AnBn(1,:),'r')
ylabel('An')
xlabel('N')


figure
scatter(AnBn(3,:),AnBn(2,:))
ylabel('Bn')
xlabel('N')

funk:
function [y] = funk(x)
T=3;
x1=1.0;
x2=x1+0.5*pi;


if (x<0)
    while (x<0)
        x=x+T;
    end
elseif (x>T)
    while (x>T)
        x=x-T;
    end
end

if (0<=x && x<x1)
    y=0;
elseif (x1<=x && x<=x2)
    y=sin(2*(x-x1)).^2;
    
elseif (x2<x && x<=T)
    y=0;
end
end

Answer 1

[Benjamin Thompson]

The fourier series coefficients should be divided by pi when calculating the reconstruction:

https://mathworld.wolfram.com/FourierSeries.html

[reddlno]

And that should fix it? Just dividing coefficients a0, an, ab by pi?

[Torsten]

According to your graph, there is a factor 3 between the two curves ...