# How to show that $f(x,y)$ are real analytical

Given a real function $f(x,y)$ on $R^2$, we know that (from wiki) it is called real analytic if it is locally given by a convergent power series.

My question is that whether there has some principle to show that $f(x,y)$ is real analytic or not. A heuristic example are also helpful.

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