List questions from analytic-functions

Published on 15 Apr 2021 - 14:50

78

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Prove or disprove : The limit $\lim_{n\rightarrow\infty}z^3_n$ exists if and only if the limit $\lim_{n\rightarrow\infty}z_n$ exists

Published on 15 Apr 2021 - 22:23

166

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Why does rational dependence of $f'$ on $f$ imply that $f$ is real-analytic?

Published on 30 Mar 2026 - 5:00

96

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Well-definedness of complex $\sin^{-1}$

Published on 17 Apr 2021 - 8:48

33

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Why does rational dependence of second derivatives on lower-order derivatives imply the map is real-analytic?

Published on 30 Mar 2026 - 2:24

138

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Integral of an analytic complex function inside a closed disk

Published on 17 Apr 2021 - 9:34

305

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Holomorphic injective function has non-zero derivative

Published on 18 Apr 2021 - 8:51

45

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Prove/ give counter example: $\lim_{z\to\ w}f(z)=\infty\iff\lim_{z\to\ w}Re(f)=lim_{z\to\ w}Im(f)=\infty$

Published on 18 Apr 2021 - 13:11

59

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The intersection of zero loci of a family of real analytic functions

Published on 21 Apr 2021 - 11:56

87

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Coefficients of taylor series of an analytic function about different centers.

Published on 22 Apr 2021 - 2:06

548

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Schwarz Lemma application problem

Published on 25 Apr 2021 - 17:23

29

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$\forall x_0 ∈ (a,b) \exists c \in (a, x_0), d \in (x_0, b), c_0, d_0$, such that $\forall x \in (c,d) \exists \frac{|f^{(n)}(x)|}{n!} \leq c_0d_0^n$

Published on 27 Apr 2021 - 2:34

65

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A holomorphic function is identically zero

Published on 27 Apr 2021 - 6:30

115

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How to extend analytic function

Published on 02 May 2021 - 9:12

50

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Analytic image of conjugate of a point

Published on 02 May 2021 - 22:24

List Question

Question about analytic function at complex field

Prove or disprove : The limit $\lim_{n\rightarrow\infty}z^3_n$ exists if and only if the limit $\lim_{n\rightarrow\infty}z_n$ exists

Why does rational dependence of $f'$ on $f$ imply that $f$ is real-analytic?

Well-definedness of complex $\sin^{-1}$

Why does rational dependence of second derivatives on lower-order derivatives imply the map is real-analytic?

Integral of an analytic complex function inside a closed disk

Holomorphic injective function has non-zero derivative

Prove/ give counter example: $\lim_{z\to\ w}f(z)=\infty\iff\lim_{z\to\ w}Re(f)=lim_{z\to\ w}Im(f)=\infty$

The intersection of zero loci of a family of real analytic functions

Coefficients of taylor series of an analytic function about different centers.

Schwarz Lemma application problem

$\forall x_0 ∈ (a,b) \exists c \in (a, x_0), d \in (x_0, b), c_0, d_0$, such that $\forall x \in (c,d) \exists \frac{|f^{(n)}(x)|}{n!} \leq c_0d_0^n$

A holomorphic function is identically zero

How to extend analytic function

Analytic image of conjugate of a point

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