Question

Find the Taylor series about $z=0$ and the Laurent series about $z=-3$

score 961 · Answer 1 · 2026-04-14 15:27:37

961

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Find the Taylor series about $z=0$ and the Laurent series about $z=-3$

Published on 14 Apr 2026 - 15:27

score 31 · Answer 2 · 2026-04-11 01:21:01

31

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Explanation of a step in proof of Triangle Inequality for Contour Integrals

Published on 11 Apr 2026 - 1:21

score 121 · Answer 3 · 2026-04-16 13:04:33

121

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If $P$ is a polynomial, then there exists $z_0$ such that $|z_0|=1$ and $|P(z_0)-\frac{1}{z_0}|\geq 1$.

Published on 16 Apr 2026 - 13:04

score 46 · Answer 4 · 2026-04-10 19:38:48

46

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Order of a $0$ of a rational function

Published on 10 Apr 2026 - 19:38

score 1.1k · Answer 5 · 2026-04-14 15:01:05

1.1k

Views

Holomorphic functions which preserve orientation

Published on 14 Apr 2026 - 15:01

score 127 · Answer 6 · 2026-04-23 15:37:19

127

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Runge theorem application? (From conway book)

Published on 23 Apr 2026 - 15:37

score 964 · Answer 7 · 2026-04-17 08:31:02

964

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Holomorphic function on the unit disc

Published on 17 Apr 2026 - 8:31

score 86 · Answer 8 · 2026-04-12 20:08:24

86

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Is $f(x + iy) = x + 2i (x+y)$ holomorphic?

Published on 12 Apr 2026 - 20:08

score 289 · Answer 9 · 2026-04-15 10:44:51

289

Views

Rudin's RCA: proof of Theorem 1.40

Published on 15 Apr 2026 - 10:44

score 569 · Answer 10 · 2026-04-12 19:49:10

569

Views

Corollary of Liouville's Theorem

Published on 12 Apr 2026 - 19:49

score 474 · Answer 11 · 2026-04-14 04:47:07

474

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using the mean-value property for holomorphic functions

Published on 14 Apr 2026 - 4:47

score 534 · Answer 12 · 2026-04-16 18:54:57

534

Views

Proving $\int_0^r{(r^m-x^m)^{1/m}dx}=\frac{\Gamma\left(\frac{1}{m}+1\right)\Gamma\left(\frac{1}{m}+1\right)}{\Gamma\left(\frac{2}{m}+1\right)}r^2$

Published on 16 Apr 2026 - 18:54

score 1.1k · Answer 13 · 2026-04-10 17:46:03

1.1k

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Integral of holomorphic function is again holomorphic

Published on 10 Apr 2026 - 17:46

score 49 · Answer 14 · 2026-04-12 08:40:24

49

Views

Provide parametisations for the triangle with vertices $1, 2i$ and $-1$

Published on 12 Apr 2026 - 8:40

score 97 · Answer 15 · 2026-04-20 14:10:23

97

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One missing ingredient to show that $F(z)=\frac{f(z)-f(z_0)}{z-z_0}$ with $F(z_0) = f'(z_0)$ is analytic.

Published on 20 Apr 2026 - 14:10

List Question

Find the Taylor series about $z=0$ and the Laurent series about $z=-3$

Explanation of a step in proof of Triangle Inequality for Contour Integrals

If $P$ is a polynomial, then there exists $z_0$ such that $|z_0|=1$ and $|P(z_0)-\frac{1}{z_0}|\geq 1$.

Order of a $0$ of a rational function

Holomorphic functions which preserve orientation

Runge theorem application? (From conway book)

Holomorphic function on the unit disc

Is $f(x + iy) = x + 2i (x+y)$ holomorphic?

Rudin's RCA: proof of Theorem 1.40

Corollary of Liouville's Theorem

using the mean-value property for holomorphic functions

Proving $\int_0^r{(r^m-x^m)^{1/m}dx}=\frac{\Gamma\left(\frac{1}{m}+1\right)\Gamma\left(\frac{1}{m}+1\right)}{\Gamma\left(\frac{2}{m}+1\right)}r^2$

Integral of holomorphic function is again holomorphic

Provide parametisations for the triangle with vertices $1, 2i$ and $-1$

One missing ingredient to show that $F(z)=\frac{f(z)-f(z_0)}{z-z_0}$ with $F(z_0) = f'(z_0)$ is analytic.

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