Let \(A\) and \(B\) be the radii of convergence of \(\sum a_kz^k\) and \(\sum b_kz^k\).
Prove that the radius of convergence of \(\sum a_kb_kz^k\) is at least \(AB\).
Give an example for which the inequality is strict.
Coefficientwise products of power series and strictness
P-WESCA12-II1
- Area
- Complex Analysis
- Seen at
- WESLEYAN
- Years
- 2012
- Status
- draft