Convergent power series/R/Taylor series/Coincidence/Fact/Proof

Proof

That ${}f$ is infinitely often differentiable, follows directly from fact by induction. Therefore, the Taylor series exists in particular in the point ${}0$. Hence, we only have to show that the ${}n$-th derivative has ${}c_{n}n!$ as its value. But this follows also from fact.

To fact