List questions from cauchy-integral-formula

Published on 03 May 2021 - 16:16

179

Views

In the proof of Cauchy Integral Theorem, transforming $dz$ to polar coordinates drops $dr$ term, why?

Published on 04 May 2021 - 18:21

270

Views

$\int\limits_{-\infty}^\infty \left(f_T(\frac{x-\mu}{1+\Psi/2})-f_T(\frac{x+\mu}{1-\Psi/2})\right)\frac{x\gamma}{(x-x_{0})^{2}+\gamma^2/4}dx$

Published on 04 May 2021 - 20:06

166

Views

Bounded holomorphic function over unit disk uniquely determines a bounded function on the boundary by taking the limit

Published on 08 May 2021 - 5:52

456

Views

Applying Cauchy-Goursat Theorem

Published on 08 May 2021 - 15:08

190

Views

Solve the integral $\int^{+\infty}_0\frac{x\sin x}{1+x^4}dx$ using complex analysis

Published on 10 May 2021 - 15:05

56

Views

Cauchy's differentiation formula consequences

Published on 11 May 2021 - 15:56

307

Views

Complex line integral: $\int_{|z|=1}\frac{z^2+2}{z(z-3)}dz$

Published on 11 May 2021 - 19:56

96

Views

Study the improper integral for convergence and absolute convergence

Published on 12 May 2021 - 1:35

73

Views

Compute $\int_{\{|z|=4\}}\frac{z^2+2}{(z-3)^2}dz$

Published on 12 May 2021 - 11:39

196

Views

Prove $\int_{|z|=1}\frac{P_n(z)}{z^{n+1}(z-a)}dz=0$

Published on 13 May 2021 - 6:36

518

Views

Finding the coefficient of the Laurent Series using the integral formula

Published on 25 May 2021 - 17:01

126

Views

Use of Stone-Weierstrass Theorem for $1/z$ on complex circle

Published on 23 Feb 2026 - 15:32

186

Views

When can functions of a complex variable be integrated 'normally'?

Published on 27 May 2021 - 15:58

516

Views

Cauchy's integral Theorem for functions with removable singularities

Published on 28 May 2021 - 19:00

List Question

Cauchy Integral Question

In the proof of Cauchy Integral Theorem, transforming $dz$ to polar coordinates drops $dr$ term, why?

$\int\limits_{-\infty}^\infty \left(f_T(\frac{x-\mu}{1+\Psi/2})-f_T(\frac{x+\mu}{1-\Psi/2})\right)\frac{x\gamma}{(x-x_{0})^{2}+\gamma^2/4}dx$

Bounded holomorphic function over unit disk uniquely determines a bounded function on the boundary by taking the limit

Applying Cauchy-Goursat Theorem

Solve the integral $\int^{+\infty}_0\frac{x\sin x}{1+x^4}dx$ using complex analysis

Cauchy's differentiation formula consequences

Complex line integral: $\int_{|z|=1}\frac{z^2+2}{z(z-3)}dz$

Study the improper integral for convergence and absolute convergence

Compute $\int_{\{|z|=4\}}\frac{z^2+2}{(z-3)^2}dz$

Prove $\int_{|z|=1}\frac{P_n(z)}{z^{n+1}(z-a)}dz=0$

Finding the coefficient of the Laurent Series using the integral formula

Use of Stone-Weierstrass Theorem for $1/z$ on complex circle

When can functions of a complex variable be integrated 'normally'?

Cauchy's integral Theorem for functions with removable singularities

Trending Questions

Popular # Hahtags

Popular Questions