Thm 37.1
For we can prove
Thm 37.2
For uniform limit where is continue and point-wise, we can say .
Thm 37.3
For is uniform limit and in Metric Space is uniform limit.
Def 37.4 Cauchy-Hadamard theorem
Props 37.5
are uniformly Cauchy on
Cor 37.6
uniformly converge to on and convergent.
Lemma 37.7
Thm 37.8
let and
Then on , is
- Well defined
- continue
- differentiable
- integrable
Def 38.1
Remark 38.2
Radius of convergent comes from complex inequality.