# Math Help - finding a continues series for convergence in L2

1. ## finding a continues series for convergence in L2

i have a function
f(x)=
1 for x>0
0 for x=0

-1 for x<0

i need to find a series which belongs to C[T] for which fn(x) converges to f(x) in L2 norm

in other words

||fn(x)-f||_{L_2(T)} ->0 then n->infinity

how i tried:

i have dissamble the norm into the integral definition of L2(T)
so the integral is from -pi to +pi
and inside we have |fn-f|^2

then i splited the integral into to parts ,because f=1 for x>0 and f=-1 for x<0.

i tried to draw a formula that will make 1/n type in the end but
the continuety doesnt allow

2. ## re: finding a continues series for convergence in L2

Your function is not defined for x in [-1, 0) or (0,1]?

ohhhh sorry
i ment
f(x)=
1 x>0
0 x=0
-1 x<0