Zophikel's user avatar
Zophikel's user avatar
Zophikel's user avatar
Zophikel
  • Member for 7 years, 9 months
  • Last seen more than a month ago
7 votes
2 answers
351 views

About the proof that $\int_0^\infty\frac{dx}{x^2+6x+8} =\frac12\log2$ via residue formula

7 votes
4 answers
1k views

Evaluating $\int_{0}^{\infty} \frac{1}{a_{n}x^{n} + ... + a_{2}x^{2} + a_{o}}dx$ via Residue Theory?

5 votes
1 answer
181 views

Verifying a Series Solution to Dirichlet's Problem via separation of variables

4 votes
1 answer
341 views

Summing series in the form: $\sum_{n=\infty}^{\infty}f(n)$ via Complex Methods?

4 votes
3 answers
732 views

Converting an $\prod_{n=2}(1+(-1)^{n}\frac{1}{n})$ into an Infinite Series to determine Convergence?

4 votes
2 answers
670 views

Intuition behind $m(b-a) \leq L(P,f) \leq U(P,f) \leq M(b-a)$

3 votes
0 answers
175 views

Verifying my proof of Liouville's theorem?

3 votes
1 answer
94 views

Justifying Calculations on $f(n)=\frac{1}{2 \pi}\int_{-\pi}^{\pi}\theta e^{-in \theta} d \theta$

3 votes
1 answer
736 views

Verifying $|F(r)| \geq \frac{1}{1-r}\log(\frac{1}{1-r}) $ and $|F(re^{i \theta})| \geq c_{q/r}\frac{1}{1-r}\log({\log(\frac{1}{1-r})})$

3 votes
1 answer
210 views

Setting up bounds for the integral $(\int_{U}|f(x,y)|^{2}dxdy)^{\frac{1}{2}}$?

3 votes
1 answer
317 views

Showing that $\int_{0}^{\infty} \frac{\cos(x)}{x^{2}+3}dx = \frac{e^{-\sqrt{3}} \pi}{2 \sqrt{3}}$ via Contour Integration?

3 votes
1 answer
221 views

Understanding the proof of convergence criterion for infinite products via the relation of series?

3 votes
1 answer
271 views

Verifying the Indictor Function:$X_{[a,b]}$ can be expressed as a Fourier Series?

3 votes
0 answers
167 views

An approach to finding the upper bound of $\int_{0}^{\pi}\frac{\sqrt[2]{Re^{i \theta}}}{4+ (Re^{i \theta})^2}iRe^{i \theta}\,\mathrm d\theta$

2 votes
0 answers
501 views

Showing that $f(z) = \frac{1}{2 \pi}\int_{0}^{2 \pi}f(Re^{i \phi})Re\left(\frac{re^{i \phi}+z}{re^{i \phi} - z}\right)d \phi$ via Complex Analysis?

2 votes
1 answer
319 views

Clarification on applying Feynman's Integration Trick to Partial Derivatives?

2 votes
1 answer
203 views

Clearification on the proof of Goursat's Theorm from Stein's Complex Analysis

2 votes
0 answers
288 views

Proving:$\frac{1}{2i}\int\limits_{-\infty}^{\infty}\frac{e^{ix}-1}{x}dx = \frac{\pi}{2}$ via Complex Methods? [duplicate]

2 votes
1 answer
413 views

Intution behind Chebyshev polynomials?

2 votes
1 answer
2k views

Proving $\nabla^2(|f|^{2})=4 |\partial f / \partial z|^2$ via a "Laplacian Approach"

2 votes
0 answers
229 views

Showing that $\int_{\gamma_R} \frac{dz}{z^4+1} = \pi $?

2 votes
1 answer
409 views

Taking $\int_{-\infty}^{\infty} \frac{e^{i \omega x}}{1 + ix}dx$ through Residue Theory?

2 votes
0 answers
89 views

Capturing integrals of the form $\int_{-\infty}^{\infty}f(x)e^{-i\omega x}dx$ through residue theory?

2 votes
2 answers
414 views

Absolute convergence of $\sum\limits_n\left( \log (1-\frac{z}{n})^{n^{k}} + \sum\limits_{m=1}^{k+1}\log e^{n^{k-m}z^m/m} \right)$?

1 vote
1 answer
110 views

Showing that $\sum_{j} f_{j}(z) \rightarrow \Psi(z)^{n}$ uniformally on compact subsets?

1 vote
0 answers
81 views

Showing that $\sum_{k=0}^{\infty}\frac{(-1)^{k}z^{n+2k}}{k!(n+k)!}2^{n+2k}$ Is Entire?

1 vote
0 answers
129 views

Motivation to consider a specific compact set to get uniform bounds on the derivatives of a holomorphic function?

1 vote
1 answer
141 views

Proving the convergence of $\bigg (\sum_{n}^{\nu} \bigg( \sum_{n}^{\chi} |\log(p_{n})+\log(q_{n})| \bigg ) \bigg )$?

1 vote
2 answers
280 views

A rough idea to prove $\int_{0}^{\infty}\frac{\sin(x)}{x}\frac{\sin(x/3)}{x/3}dx = \frac{\pi}{2} ?$

1 vote
1 answer
355 views

Showing that $\lim_{R \rightarrow \infty} \bigg(\int_{0}^{R}e^{ix^{2}}dx-e^{i \pi/4}\int_{0}^{R}e^{-r^{2}}dr \bigg)=0$?