According to Wikipedia, l'Hopital's rule is applicable only to functions from R to R, but some authors on Mathematics stack exchange seem to claim that it's applicable also to functions from C to C. What should I believe? Which source is more reliable?
2026-04-23 10:38:46.1776940726
Should I trust Wikipedia or Mathematics stack exchange concerning l'Hopital's rule?
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Complex versions of l'Hôpital's Rule can be found in many Complex Analysis texts, e.g. Levinson and Redheffer Example 7.1:
Let $f$ and $g$ be analytic in a domain $D$ and not identically $0$. If $f(\alpha) = g(\alpha) = 0$ at a point $\alpha$ of $D$, show that
$$ \lim_{z \to \alpha} \frac{f(z)}{g(z)} = \lim_{z \to \alpha} \frac{f'(z)}{g'(z)}, $$ the value $\infty$ being allowed in both cases.