Ostrowski–Hadamard gap theorem

In mathematics, the Ostrowski–Hadamard gap theorem is a result about the analytic continuation of complex power series whose non-zero terms are of orders that have a suitable "gap" between them. Such a power series is "badly behaved" in the sense that it cannot be extended to be an analytic function anywhere on the boundary of its disc of convergence. The result is named after the mathematicians Alexander Ostrowski and Jacques Hadamard.