# Sept. 10, 2002
# Fourier Series expansion of a constant function on the interval [0,4]
# 
> N:=100;L:=4;f:=1;
> Int(f*sin(i*Pi/L)*x,x=0..L);
> for i from 1 to N do a[i]:=(2/L)*evalf(Int(f*sin(i*Pi*x/L),x=0..L));
> od:
> i:='i';
> for n from 1 to N do v[n]:=sum(a[i]*sin(i*Pi*x/L),i=1..n) od:
> plot([f,v[1],v[5],v[10]],x=0..L,color=[red,blue,green,black]);
> 
> plot([f,v[10],v[30],v[50]],x=0..L,color=[red,blue,green,black]);
> plot([f,v[25],v[50],v[75],v[100]],x=0..L,color=[red,blue,green,orange,
> black]);
> plot([f,v[100]],x=0..L,color=[red,black]);
>