Let \(f\) and \(g\) be analytic on \(U\subset \mathbb{C}\) and \(f=g\) on a subset with one accumulation point, then \(f=g\) on \(U\). [1, Corollary 1.2.7]

Remark

The same is true for real analytic functions .

References Link to heading

S. Krantz and H. Parks, A Primer of Real Analytic Functions. Boston, MA: Birkhäuser Boston, 2002. doi:10.1007/978-0-8176-8134-0