Question

Suppose $f:\mathbb{D}\rightarrow\mathbb{C}$ is analytic such that $|f|<2$. Also, suppose that $f''(0)=4i$. Find the value of $f(i/2)$.

score 93 · Answer 1 · 2021-10-12 19:24:50

Suppose $f:\mathbb{D}\rightarrow\mathbb{C}$ is analytic such that $|f|<2$. Also, suppose that $f''(0)=4i$. Find the value of $f(i/2)$.

score 107 · Answer 2 · 2026-03-27 20:54:05

107

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trying to understand analytic continuation (2 scenarios)

Published on 27 Mar 2026 - 20:54

score 62 · Answer 3 · 2026-03-30 06:47:38

62

Views

If $f$ is analytic on an open and simply-connected subset of $\Bbb{C}$, and if $\cos{f}$ is constant, then must $f$ also be constant?

Published on 30 Mar 2026 - 6:47

score 314 · Answer 4 · 2026-03-27 03:42:14

314

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Existence of real analytic diffeomorphisms with prescribed values on a finite set

Published on 27 Mar 2026 - 3:42

score 20 · Answer 5 · 2021-10-23 12:08:47

20

Views

Prove that $f(a) = \frac{1}{2\pi i} \int_\gamma f(z) (\frac{1}{z-a} - \frac{1}{z-\frac{r^2}{\overline{a}}})$ where $0<a<r$

Published on 23 Oct 2021 - 12:08

score 241 · Answer 6 · 2026-03-30 06:50:12

241

Views

Holomorphic is much stronger than real differentiable in a neighbourhood. What about analytic?

Published on 30 Mar 2026 - 6:50

score 116 · Answer 7 · 2026-03-27 20:54:05

116

Views

Can this type of function, defined on the closed unit disk, be analytically continued into the complex plane?

Published on 27 Mar 2026 - 20:54

score 32 · Answer 8 · 2021-11-03 00:30:01

32

Views

Complex Analysis: Bounded Analytic Function & Continuously Extend

Published on 03 Nov 2021 - 0:30

score 54 · Answer 9 · 2026-03-27 01:13:57

54

Views

Proving whether a complex function is analytical help!

Published on 27 Mar 2026 - 1:13

score 41 · Answer 10 · 2021-11-30 00:42:28

41

Views

Making sense of Identity Theorem in application

Published on 30 Nov 2021 - 0:42

score 173 · Answer 11 · 2026-03-27 04:38:10

173

Views

How can I find all holomorphic functions $f:\mathbb C \to \mathbb C$ having $f=u+iv$ with $v(x,y)=u^2(x,y)$

Published on 27 Mar 2026 - 4:38

score 37 · Answer 12 · 2021-12-02 22:45:53

37

Views

Is the function $f(w) = e^{-w}w^{z-1}$ holomorphic for $z \in \mathbb{C}$

Published on 02 Dec 2021 - 22:45

score 50 · Answer 13 · 2026-02-23 04:45:44

50

Views

Could non-smooth time-limited functions been Analytical?

Published on 23 Feb 2026 - 4:45

score 127 · Answer 14 · 2026-03-28 03:55:29

127

Views

$f$ analytic in $\overline{\mathbb{D}}$ s.t $\int_{|z|=1}|f(z)-z||dz|\leq\frac{1}{100}$. Prove that $f$ has at least one zero in $\mathbb{D}$.

Published on 28 Mar 2026 - 3:55

score 64 · Answer 15 · 2021-12-06 12:14:04

64

Views

$\int_C|f_n(z)||dz|\leq M$ for each $f_n$. Prove $\{f_n\}$ has a subsequence converging uniformly on compact subsets of $D$.

Published on 06 Dec 2021 - 12:14

List Question

Suppose $f:\mathbb{D}\rightarrow\mathbb{C}$ is analytic such that $|f|<2$. Also, suppose that $f''(0)=4i$. Find the value of $f(i/2)$.

trying to understand analytic continuation (2 scenarios)

If $f$ is analytic on an open and simply-connected subset of $\Bbb{C}$, and if $\cos{f}$ is constant, then must $f$ also be constant?

Existence of real analytic diffeomorphisms with prescribed values on a finite set

Prove that $f(a) = \frac{1}{2\pi i} \int_\gamma f(z) (\frac{1}{z-a} - \frac{1}{z-\frac{r^2}{\overline{a}}})$ where $0<a<r$

Holomorphic is much stronger than real differentiable in a neighbourhood. What about analytic?

Can this type of function, defined on the closed unit disk, be analytically continued into the complex plane?

Complex Analysis: Bounded Analytic Function & Continuously Extend

Proving whether a complex function is analytical help!

Making sense of Identity Theorem in application

How can I find all holomorphic functions $f:\mathbb C \to \mathbb C$ having $f=u+iv$ with $v(x,y)=u^2(x,y)$

Is the function $f(w) = e^{-w}w^{z-1}$ holomorphic for $z \in \mathbb{C}$

Could non-smooth time-limited functions been Analytical?

$f$ analytic in $\overline{\mathbb{D}}$ s.t $\int_{|z|=1}|f(z)-z||dz|\leq\frac{1}{100}$. Prove that $f$ has at least one zero in $\mathbb{D}$.

$\int_C|f_n(z)||dz|\leq M$ for each $f_n$. Prove $\{f_n\}$ has a subsequence converging uniformly on compact subsets of $D$.

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