List questions from complex-analysis

Published on 12 Apr 2026 - 15:10

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Show that function is integrable

Published on 12 Apr 2026 - 1:08

325

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Mapping the unit disc to $\mathbb{C}\setminus\{z\in\mathbb{C}:\Re(z)=0,|\Im(z)|\geq1\}$

Published on 16 Apr 2026 - 12:39

398

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Find sequence of complex numbers $\{z_k\}$ such that $z_k \to 0$ and $ e^{1/z_k} \to 2+i$

Published on 14 Apr 2026 - 2:27

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Use of a Laplace Transform to solve Abel's Integral Equation

Published on 14 Apr 2026 - 4:45

191

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Deriving $|\sum\limits_{k=0}^n (-1)^k \binom{n}{k}\binom{2n}{k}|\leq (\frac{16\sqrt 3}{9})^n $ where $|(z-1)^2(z+1)|\leq \frac{16\sqrt{3}}{9}$

Published on 25 Mar 2026 - 17:44

147

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Suppose $z=x+iy$, prove that $\lim\limits_{n\to\infty}(1+\frac{z}{n})^n=e^x(\cos{y}+i\sin{y})$?

Published on 16 Apr 2026 - 7:27

903

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Singularities of $\,\mathrm{e}^{-1/z^2}$

Published on 14 Apr 2026 - 11:37

1.2k

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Usage of Schwarz Reflection Principle to Study Conformal Equivalence of Annuli

Published on 14 Apr 2026 - 13:42

94

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Complex Integral only with Exponentials.

Published on 13 Apr 2026 - 15:13

41

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Complex integral over $\mathbb{R}$

Published on 17 Apr 2026 - 3:10

138

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Does the Taylor series of $\ln(x)$ about $1$ allow domain extension?

Published on 15 Apr 2026 - 3:41

85

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Riemann surfaces in real analysis?

Published on 11 Apr 2026 - 7:24

188

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Domain of complex function / singularity

Published on 14 Apr 2026 - 13:22

68

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Is this the Taylor expansion of a known function?

Published on 14 Apr 2026 - 8:03

List Question

integral involving hyperbolic tangent and cosine

Show that function is integrable

Mapping the unit disc to $\mathbb{C}\setminus\{z\in\mathbb{C}:\Re(z)=0,|\Im(z)|\geq1\}$

Find sequence of complex numbers $\{z_k\}$ such that $z_k \to 0$ and $ e^{1/z_k} \to 2+i$

Use of a Laplace Transform to solve Abel's Integral Equation

Deriving $|\sum\limits_{k=0}^n (-1)^k \binom{n}{k}\binom{2n}{k}|\leq (\frac{16\sqrt 3}{9})^n $ where $|(z-1)^2(z+1)|\leq \frac{16\sqrt{3}}{9}$

Suppose $z=x+iy$, prove that $\lim\limits_{n\to\infty}(1+\frac{z}{n})^n=e^x(\cos{y}+i\sin{y})$?

Singularities of $\,\mathrm{e}^{-1/z^2}$

Usage of Schwarz Reflection Principle to Study Conformal Equivalence of Annuli

Complex Integral only with Exponentials.

Complex integral over $\mathbb{R}$

Does the Taylor series of $\ln(x)$ about $1$ allow domain extension?

Riemann surfaces in real analysis?

Domain of complex function / singularity

Is this the Taylor expansion of a known function?

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