Interactive Real Analysis
- part of Proposition 8.4.1: Derivatives of Power Series Function
Suppose
f(x) = 
an(x-c)n
is a convergent power series with radius of convergence r > 0.
Then
Context
an(x-c)n
is a convergent power series with radius of convergence r > 0.
Then
an =
ContextThe proof is a repeated application of the theorem on differentiating and integrating power series.