Question

Do any major theorems of complex analysis that require holomorphic functions fail if the function is only holomorphic up to removable singularities?

score 50 · Answer 1 · 2026-03-22 12:51:11

50

Views

Do any major theorems of complex analysis that require holomorphic functions fail if the function is only holomorphic up to removable singularities?

Published on 22 Mar 2026 - 12:51

score 46 · Answer 2 · 2016-12-15 15:33:12

46

Views

Holomorphism check for the functions $F(z)=\int_{-\infty}^\infty e^{(t-z)^2}dt$ and $G(z)=\int_{-\infty}^\infty e^{|t-z|^2}dt$

Published on 15 Dec 2016 - 15:33

score 52 · Answer 3 · 2016-12-24 14:32:12

52

Views

Inhomogeneous Equation Advice

Published on 24 Dec 2016 - 14:32

score 766 · Answer 4 · 2017-01-05 18:08:21

766

Views

Complex square root analytic with Cauchy-Riemann equations

Published on 05 Jan 2017 - 18:08

score 91 · Answer 5 · 2017-01-05 18:25:09

91

Views

Nonnegative $C^{\omega}$ function $f$ with $\int_\mathbb{R} f(t) \ dt < + \infty$ but $\lim f(x) \neq 0$

Published on 05 Jan 2017 - 18:25

score 2.5k · Answer 6 · 2017-01-07 14:50:13

2.5k

Views

If $f(z)$ is analytic at $z_0$ then it is continuous at $z_0$

Published on 07 Jan 2017 - 14:50

score 53 · Answer 7 · 2017-01-16 07:25:23

53

Views

How to prove $f(z)=f(z_0)+f^{\prime}(z_0)(z-z_0)+\eta(z-z_0)$?

Published on 16 Jan 2017 - 7:25

score 275 · Answer 8 · 2017-01-19 23:39:52

275

Views

Hypergeometric Function on the Unit Circle

Published on 19 Jan 2017 - 23:39

score 77 · Answer 9 · 2017-01-25 06:47:39

77

Views

Let $f(z) = f(z^2)$, for all $z\in\mathbb{D}$ with $f(1) = 1$, then which of the following is incorrect?

Published on 25 Jan 2017 - 6:47

score 182 · Answer 10 · 2017-02-06 09:44:12

182

Views

Multiplicity of roots of real analytic function

Published on 06 Feb 2017 - 9:44

score 81 · Answer 11 · 2017-02-08 07:09:16

81

Views

sufficient condition for analyticity

Published on 08 Feb 2017 - 7:09

score 2.7k · Answer 12 · 2026-03-22 12:23:46

2.7k

Views

real part of analytic function

Published on 22 Mar 2026 - 12:23

score 722 · Answer 13 · 2017-02-22 04:24:24

722

Views

Definition of analyticity in complex analysis

Published on 22 Feb 2017 - 4:24

score 220 · Answer 14 · 2026-03-21 19:33:23

220

Views

Question about analytic continuation of a function defined by an integral

Published on 21 Mar 2026 - 19:33

score 1.1k · Answer 15 · 2017-03-14 19:39:11

1.1k

Views

If $z\mapsto f(z)^n$ is analytic then $f$ is analytic

Published on 14 Mar 2017 - 19:39

List Question

Do any major theorems of complex analysis that require holomorphic functions fail if the function is only holomorphic up to removable singularities?

Holomorphism check for the functions $F(z)=\int_{-\infty}^\infty e^{(t-z)^2}dt$ and $G(z)=\int_{-\infty}^\infty e^{|t-z|^2}dt$

Inhomogeneous Equation Advice

Complex square root analytic with Cauchy-Riemann equations

Nonnegative $C^{\omega}$ function $f$ with $\int_\mathbb{R} f(t) \ dt < + \infty$ but $\lim f(x) \neq 0$

If $f(z)$ is analytic at $z_0$ then it is continuous at $z_0$

How to prove $f(z)=f(z_0)+f^{\prime}(z_0)(z-z_0)+\eta(z-z_0)$?

Hypergeometric Function on the Unit Circle

Let $f(z) = f(z^2)$, for all $z\in\mathbb{D}$ with $f(1) = 1$, then which of the following is incorrect?

Multiplicity of roots of real analytic function

sufficient condition for analyticity

real part of analytic function

Definition of analyticity in complex analysis

Question about analytic continuation of a function defined by an integral

If $z\mapsto f(z)^n$ is analytic then $f$ is analytic

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