Question

Existence of logarithm of holomorphic function

score 1.3k · Answer 1 · 2017-10-29 14:26:28

1.3k

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Existence of logarithm of holomorphic function

Published on 29 Oct 2017 - 14:26

score 120 · Answer 2 · 2017-10-29 14:38:47

120

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If the set of roots has cluster point then function is identically zero

Published on 29 Oct 2017 - 14:38

score 1.3k · Answer 3 · 2017-10-29 17:17:43

1.3k

Views

Applying Identity Theorem for holomorphic functions

Published on 29 Oct 2017 - 17:17

score 93 · Answer 4 · 2017-11-01 04:21:02

93

Views

$f = u+iv$ holomorphic on $D(0, 1)$ and $f(0)=0$, prove $\int_{0}^{2\pi}u(e^{it})^{4}dt \leq 36\int_{0}^{2\pi}v(e^{it})^{4}dt$

Published on 01 Nov 2017 - 4:21

score 340 · Answer 5 · 2026-03-27 11:47:53

340

Views

proving that $f(z)=1/\Gamma(z)$ is a entire function

Published on 27 Mar 2026 - 11:47

score 89 · Answer 6 · 2017-11-02 12:05:32

89

Views

Suppose on $|z|\le1$, $f(z)$ is holomorphic and $|f(z)|\le1$. Prove that $|f'(0)|\le1$

Published on 02 Nov 2017 - 12:05

score 146 · Answer 7 · 2017-11-06 22:13:48

146

Views

Rank of the differential of a holomorphic function

Published on 06 Nov 2017 - 22:13

score 143 · Answer 8 · 2017-11-08 08:47:12

Holomorphic function in a region symmetric about origin which takes real values on some non-empty interval intersection with the region

score 204 · Answer 9 · 2017-11-10 09:05:16

204

Views

If $f$ is a continuous analytic function on a unit disc about the origin $D\setminus\{0\}$, then $f$ is also analytic at $0$.

Published on 10 Nov 2017 - 9:05

score 207 · Answer 10 · 2026-03-27 04:34:33

207

Views

function ${\displaystyle \varphi }$ such that ${\displaystyle \varphi (\varphi (u))=\exp(u)}$

Published on 27 Mar 2026 - 4:34

score 258 · Answer 11 · 2017-11-12 00:18:21

258

Views

Proving the function $g$, defined by an integral, is holomorphic

Published on 12 Nov 2017 - 0:18

score 67 · Answer 12 · 2017-11-12 18:34:09

67

Views

No Sequence of polynomials converging to $f(z)= \frac{1}{z}$ on given compact set $K$

Published on 12 Nov 2017 - 18:34

score 114 · Answer 13 · 2017-11-12 19:23:04

114

Views

A problem on Runge theorem in complex analysis

Published on 12 Nov 2017 - 19:23

score 942 · Answer 14 · 2017-11-13 08:36:54

942

Views

Find all harmonic functions of the form $u(x; y) = h(x^2 + y^2).$

Published on 13 Nov 2017 - 8:36

score 144 · Answer 15 · 2017-11-13 17:41:30

144

Views

Finding all Harmonic functions on given domain

Published on 13 Nov 2017 - 17:41

List Question

Existence of logarithm of holomorphic function

If the set of roots has cluster point then function is identically zero

Applying Identity Theorem for holomorphic functions

$f = u+iv$ holomorphic on $D(0, 1)$ and $f(0)=0$, prove $\int_{0}^{2\pi}u(e^{it})^{4}dt \leq 36\int_{0}^{2\pi}v(e^{it})^{4}dt$

proving that $f(z)=1/\Gamma(z)$ is a entire function

Suppose on $|z|\le1$, $f(z)$ is holomorphic and $|f(z)|\le1$. Prove that $|f'(0)|\le1$

Rank of the differential of a holomorphic function

Holomorphic function in a region symmetric about origin which takes real values on some non-empty interval intersection with the region

If $f$ is a continuous analytic function on a unit disc about the origin $D\setminus\{0\}$, then $f$ is also analytic at $0$.

function ${\displaystyle \varphi }$ such that ${\displaystyle \varphi (\varphi (u))=\exp(u)}$

Proving the function $g$, defined by an integral, is holomorphic

No Sequence of polynomials converging to $f(z)= \frac{1}{z}$ on given compact set $K$

A problem on Runge theorem in complex analysis

Find all harmonic functions of the form $u(x; y) = h(x^2 + y^2).$

Finding all Harmonic functions on given domain

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