Let $f$ be an entire function s.t. $F(z) = \lim_{n\to\infty} f^{(n)}(z)$ exists for all $z$ with local uniform convergence. What can we say about $F$?

score 148 · Answer 14 · 2026-02-24 21:29:32

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Is $\{f_n \}$ uniformly convergent on $[0,1]\ $?

Published on 24 Feb 2026 - 21:29

score 45 · Answer 15 · 2020-07-18 15:06:41

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Uniform convergence implies $\sum \int f_n = \int \sum f_n$, what about the the converse?

Published on 18 Jul 2020 - 15:06

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Let $f$ be an entire function s.t. $F(z) = \lim_{n\to\infty} f^{(n)}(z)$ exists for all $z$ with local uniform convergence. What can we say about $F$?

Is $\{f_n \}$ uniformly convergent on $[0,1]\ $?

Uniform convergence implies $\sum \int f_n = \int \sum f_n$, what about the the converse?

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