Question

Let $f$ be analytic and Im$f(z)>0$. Show $|\frac{f(z)-f(z_0)}{f(z)-\overline{f(z_0)}}|\leq|\frac{z-z_0}{z-\overline{z_0}}|$.

score 214 · Answer 1 · 2026-03-28 00:30:56

214

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Let $f$ be analytic and Im$f(z)>0$. Show $|\frac{f(z)-f(z_0)}{f(z)-\overline{f(z_0)}}|\leq|\frac{z-z_0}{z-\overline{z_0}}|$.

Published on 28 Mar 2026 - 0:30

score 110 · Answer 2 · 2026-03-27 19:15:26

110

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Let $ f: (a, b) \to\mathbb R $ a function of class $ C^{\infty} $ that satisfies the following condition: given $ K \subset (a, b) $ compact...

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score 138 · Answer 3 · 2021-08-09 18:24:37

138

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score 203 · Answer 4 · 2026-03-27 20:54:01

203

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349

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47

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score 107 · Answer 7 · 2026-03-28 02:07:56

107

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Does there exist $z_0 \notin \{a_n\}_{n \geq 1}$ such that $f(z_0) = 0\ $?

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58

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score 153 · Answer 9 · 2026-03-30 05:01:59

153

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score 152 · Answer 10 · 2026-03-26 04:51:44

152

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score 41 · Answer 11 · 2021-08-21 04:04:26

41

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185

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score 132 · Answer 13 · 2026-03-26 23:09:29

132

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score 883 · Answer 14 · 2021-08-25 16:57:48

883

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score 44 · Answer 15 · 2021-08-26 15:58:15

Find all analytic functions in the disk $|z-2|<2$ such that $f \left(2+\frac{1}{n} \right) = \frac{1-n}{5n+3} + \sin{\left(\frac{n \pi}{2} \right)}$

List Question

Let $f$ be analytic and Im$f(z)>0$. Show $|\frac{f(z)-f(z_0)}{f(z)-\overline{f(z_0)}}|\leq|\frac{z-z_0}{z-\overline{z_0}}|$.

Let $ f: (a, b) \to\mathbb R $ a function of class $ C^{\infty} $ that satisfies the following condition: given $ K \subset (a, b) $ compact...

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Does there exist $z_0 \notin \{a_n\}_{n \geq 1}$ such that $f(z_0) = 0\ $?

How to show directly that $T(G \setminus \{a\})$ is open?

Is $ z / (e^z - 1) $ analytic in $ |z| < \pi $?

Why is the image of a subanalytic set through a proper analytic map subanalytic?

maximum of analytic function at certain point

Finding a Möbius transformation sending a set onto the open unit disk.

Show that $f^*$ is analytic on $\overline {G}.$

Where are the poles of the Riemann zeta function located?

Find all analytic functions in the disk $|z-2|<2$ such that $f \left(2+\frac{1}{n} \right) = \frac{1-n}{5n+3} + \sin{\left(\frac{n \pi}{2} \right)}$

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