a:=m->subs(an,n=m);
a(0):=a0;
b:=m->subs(bn,n=m);
Cesaro:=N->a(0)+(sum(a(n)*(N+1-n)*cos(n*PI*x/L)+b(n)*(N+1-n)*sin(n*PI*x/L),n=1..N))/(N+1);
plot(f1,Cesaro(5),x=-5..5)
m\mapsto \mathrm{subs}\left(\mathrm{an},n=m\right)
-\frac{1}{2}
m\mapsto \mathrm{subs}\left(\mathrm{bn},n=m\right)
N\mapsto a\left(0\right)+\frac{\sum
_{n=1}^N\left(a\left(n\right)\,\left(N+1-n\right)\,\cos\left(\frac{n\,\pi
\,x}{L}\right)+b\left(n\right)\,\left(N+1-n\right)\,\sin\left(\frac{n\,\pi
\,x}{L}\right)\right)}{N+1}
a:=m->subs(an,n=m);
a(0):=a0;
b:=m->subs(bn,n=m);
Cesaro:=N->a(0)+(sum(a(n)*(N+1-n)*cos(n*PI*x/L)+b(n)*(N+1-n)*sin(n*PI*x/L),n=1..N))/(N+1);
plot(f1,Cesaro(15),x=-5..5)
a:=m->subs(an,n=m);
a(0):=a0;
b:=m->subs(bn,n=m);
Cesaro:=N->a(0)+(sum(a(n)*(N+1-n)*cos(n*PI*x/L)+b(n)*(N+1-n)*sin(n*PI*x/L),n=1..N))/(N+1);
plot(f1,Cesaro(30),x=-5..5)
