List questions from complex-analysis

Published on 14 Apr 2026 - 9:56

1k

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Proving $\int_0^\infty e^{-(1-a^2)x^2} \cos(2ax^2)dx = \frac{\sqrt{\pi}}{2(1+a^2)}$

Published on 29 Apr 2026 - 12:49

98

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Normal Set in Space of Holomorphic Functions

Published on 14 Apr 2026 - 20:51

568

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Arc contribution in $\int_{-\infty}^\infty \mathrm{d}z \frac{e^{-z^2}}{z-1}$

Published on 16 Apr 2026 - 7:30

424

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The roots of a polynomial in the first quadrant

Published on 13 Apr 2026 - 15:51

452

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Convexity of $\frac x{\sin x},\,\forall x\in[0,\pi)$

Published on 13 Apr 2026 - 4:35

71

Views

A Rouché's Theorem application

Published on 14 Apr 2026 - 12:56

1k

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Convergence of a complex series on the boundary

Published on 25 Apr 2026 - 20:08

121

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Regulating divergent integrals in the complex plane

Published on 13 Apr 2026 - 12:04

60

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Existence of a holomorphic function arbitrarily large at point outside holomorphic hull and arbitrarily small inside it

Published on 13 Apr 2026 - 23:08

46

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Show that $\mathbb{C}^{*}$ is a hyperbolic type

Published on 15 Apr 2026 - 4:15

2.7k

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How to interpret $\int_0^\infty \exp(ikx) dx$ in distribution theory?

Published on 10 Apr 2026 - 9:45

281

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Image of a Domain under Möbius transformation

Published on 13 Apr 2026 - 20:58

45

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Show that, if $S $ is contractable, then any closed curve is homotopic to a constant curve

Published on 14 Apr 2026 - 9:53

52

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if $D$ denotes a circle with positive radius passing through the origin, then f maps $D$ \ {$0$} to__________

Published on 16 Apr 2026 - 1:07

List Question

Modulus of Analytic Function is Bounded Above

Proving $\int_0^\infty e^{-(1-a^2)x^2} \cos(2ax^2)dx = \frac{\sqrt{\pi}}{2(1+a^2)}$

Normal Set in Space of Holomorphic Functions

Arc contribution in $\int_{-\infty}^\infty \mathrm{d}z \frac{e^{-z^2}}{z-1}$

The roots of a polynomial in the first quadrant

Convexity of $\frac x{\sin x},\,\forall x\in[0,\pi)$

A Rouché's Theorem application

Convergence of a complex series on the boundary

Regulating divergent integrals in the complex plane

Existence of a holomorphic function arbitrarily large at point outside holomorphic hull and arbitrarily small inside it

Show that $\mathbb{C}^{*}$ is a hyperbolic type

How to interpret $\int_0^\infty \exp(ikx) dx$ in distribution theory?

Image of a Domain under Möbius transformation

Show that, if $S $ is contractable, then any closed curve is homotopic to a constant curve

if $D$ denotes a circle with positive radius passing through the origin, then f maps $D$ \ {$0$} to__________

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