Question

Is the closed form of $\sum_{n=0}^\infty n!x^n$ unique?

score 115 · Answer 1 · 2020-11-09 02:15:51

115

Views

Is the closed form of $\sum_{n=0}^\infty n!x^n$ unique?

Published on 09 Nov 2020 - 2:15

score 72 · Answer 2 · 2026-03-30 01:28:31

72

Views

When Non-Constant Analytic Functions are Real-Unbounded

Published on 30 Mar 2026 - 1:28

score 35 · Answer 3 · 2020-11-12 17:47:02

35

Views

Function $f(x,y)$ analytic with respect to both $x$ and $y$, is $\frac{\partial}{\partial y} f(x,y)$ analytic with respect to $x$?

Published on 12 Nov 2020 - 17:47

score 130 · Answer 4 · 2020-11-12 23:45:47

130

Views

Connected components of the zero set

Published on 12 Nov 2020 - 23:45

score 320 · Answer 5 · 2026-03-29 10:59:02

320

Views

Identify the isolated singularities of the $f(z) = \frac{\cos(1/z)}{(z-1)^3}$. If the isolated singularity is a pole, find its order.

Published on 29 Mar 2026 - 10:59

score 252 · Answer 6 · 2026-02-23 15:16:37

252

Views

Intuition behind the general form of the solution in Frobenius Method?

Published on 23 Feb 2026 - 15:16

score 52 · Answer 7 · 2026-03-30 01:28:39

52

Views

Examples of non-polynomial analytic homeomorphisms

Published on 30 Mar 2026 - 1:28

score 132 · Answer 8 · 2020-11-23 00:54:51

132

Views

Reading roadmap for Deligne's Equations Differentielles a Points Singuliers Reguliers

Published on 23 Nov 2020 - 0:54

score 106 · Answer 9 · 2020-11-25 10:42:49

106

Views

How are complex functions different from functions of the form $\mathbb{R}^2\rightarrow \mathbb{R}^2$?

Published on 25 Nov 2020 - 10:42

score 236 · Answer 10 · 2020-11-26 15:15:35

236

Views

What is the radius of convergence of Taylor series of $ e^{- \frac{1}{z^2}} $ about $z_0 \ne 0 $

Published on 26 Nov 2020 - 15:15

score 45 · Answer 11 · 2020-11-30 06:58:39

45

Views

Show that $f$ has a fixed point at $\overline{B_1(0)}$.

Published on 30 Nov 2020 - 6:58

score 350 · Answer 12 · 2026-03-30 03:19:01

350

Views

Function having all order derivatives that are positive is analytic

Published on 30 Mar 2026 - 3:19

score 118 · Answer 13 · 2020-12-05 06:21:38

118

Views

If $f$ is a mapping from $\overline{B_1(0)}$ to itself that is continuous and analytic, prove that $f$ has a fixed point.

Published on 05 Dec 2020 - 6:21

score 113 · Answer 14 · 2020-12-06 21:27:53

113

Views

Cauchy-Kovalevsky Theorem: Application question

Published on 06 Dec 2020 - 21:27

score 86 · Answer 15 · 2026-03-27 19:30:22

86

Views

Existence of analytic function with certain conditions

Published on 27 Mar 2026 - 19:30

List Question

Is the closed form of $\sum_{n=0}^\infty n!x^n$ unique?

When Non-Constant Analytic Functions are Real-Unbounded

Function $f(x,y)$ analytic with respect to both $x$ and $y$, is $\frac{\partial}{\partial y} f(x,y)$ analytic with respect to $x$?

Connected components of the zero set

Identify the isolated singularities of the $f(z) = \frac{\cos(1/z)}{(z-1)^3}$. If the isolated singularity is a pole, find its order.

Intuition behind the general form of the solution in Frobenius Method?

Examples of non-polynomial analytic homeomorphisms

Reading roadmap for Deligne's Equations Differentielles a Points Singuliers Reguliers

How are complex functions different from functions of the form $\mathbb{R}^2\rightarrow \mathbb{R}^2$?

What is the radius of convergence of Taylor series of $ e^{- \frac{1}{z^2}} $ about $z_0 \ne 0 $

Show that $f$ has a fixed point at $\overline{B_1(0)}$.

Function having all order derivatives that are positive is analytic

If $f$ is a mapping from $\overline{B_1(0)}$ to itself that is continuous and analytic, prove that $f$ has a fixed point.

Cauchy-Kovalevsky Theorem: Application question

Existence of analytic function with certain conditions

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