Suppose we have an even function, $f$, defined on the real line. Suppose this function admits an analytic continuation, defined on the whole of $\mathbb{C}$. Does this imply that said analytic continuation is also even?
2026-02-23 06:28:44.1771828124
Is the analytic continuation of an even function even?
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Hint: If $F$ is the analytic continuation of $f$ to $\mathbb C$, what can you say about the zeros of $F(z)-F(-z)$?