In[]:=
Remove["Global`*"];​​dist=NormalDistribution[0,1];​​n=20;​​SeedRandom[4567];​​data=Sort[RandomVariate[dist,n]];​​F0[x_]:=CDF[dist,x]​​KolmogorovSmirnovTest[data,dist,"TestData"]​​dn=%[[1]]
Out[]=
{0.170791,0.547454}
Out[]=
0.170791
In[]:=
cdfK[x_]:=1+2Sum[
k
(-1)
*Exp[-2
2
k
*
2
x
],{k,1,∞}];​​1-cdfKdn*
n
+
1
6*
n
+
dn*
n
-1
4n

Out[]=
0.547214