Question

$U$ $\setminus$ $K$ is an open connected set

score 147 · Answer 1 · 2026-04-12 12:19:46

147

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$U$ $\setminus$ $K$ is an open connected set

Published on 12 Apr 2026 - 12:19

score 1.2k · Answer 2 · 2026-04-16 12:52:58

1.2k

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Evaluating $ \int_0^\pi \frac{\cos{n\theta}}{1 -2r\cos{\theta}+r^2} d\theta $

Published on 16 Apr 2026 - 12:52

score 43 · Answer 3 · 2026-04-23 02:36:37

43

Views

Show $(\frac{x^n}{n!})'=\frac{x^{n-1}}{(n-1)!}$

Published on 23 Apr 2026 - 2:36

score 41 · Answer 4 · 2026-04-11 18:02:47

41

Views

complex integral , with singularity ${1\over \pi}$

Published on 11 Apr 2026 - 18:02

score 704 · Answer 5 · 2026-04-13 06:48:10

704

Views

Harmonic Functions and Partial Derivatives with Chain Rule (Complex Variables)

Published on 13 Apr 2026 - 6:48

score 402 · Answer 6 · 2026-04-16 10:38:59

402

Views

If $f$ is an entire function such that for each $\theta$, $|f(re^{i\theta})|\rightarrow \infty$ as $r\rightarrow \infty$

Published on 16 Apr 2026 - 10:38

score 88 · Answer 7 · 2026-04-16 05:55:31

Let $\gamma_r(t) = 1+re^{it}$ for $0\leq t \leq \pi/4$. Calculate $\lim\limits_{r\rightarrow 0+} \int_{\gamma_r} \frac{\cos (\pi z)}{\log z}$

score 528 · Answer 8 · 2026-04-10 16:44:41

528

Views

Complex polynomial that has no roots in the closed unit disc

Published on 10 Apr 2026 - 16:44

score 38 · Answer 9 · 2026-04-15 06:15:44

38

Views

If $\int f(z) dz = 0$ for every closed triangular region $T ⊂ U$. Show that $f$ is holomorphic on $U$

Published on 15 Apr 2026 - 6:15

score 98 · Answer 10 · 2026-04-08 17:24:45

98

Views

Please prove the statement in description given in section 3 of Quantum Mechanics (Landau & Lifshitz).

Published on 08 Apr 2026 - 17:24

score 63 · Answer 11 · 2026-04-11 12:12:50

63

Views

Complex Analysis : A function satisfying certain conditions , a counterexample?

Published on 11 Apr 2026 - 12:12

score 35 · Answer 12 · 2026-04-16 03:40:59

35

Views

Find the radius of convergence of Maclaurin series of $(1 + z)^α$

Published on 16 Apr 2026 - 3:40

score 572 · Answer 13 · 2026-04-13 06:17:54

572

Views

Evaluating the Laurent series of $\frac{1}{\exp (z) -1 }$

Published on 13 Apr 2026 - 6:17

score 163 · Answer 14 · 2026-04-10 18:27:41

163

Views

Finding the singularities of a complex function.

Published on 10 Apr 2026 - 18:27

score 202 · Answer 15 · 2026-04-17 05:04:25

202

Views

If $f_1,...,f_k$ are given holomorphic functions and $f$ is such that $f_i/f$ is holomorphic then $g_1f_1 + \cdots + g_nf_n = gf$

Published on 17 Apr 2026 - 5:04

List Question

$U$ $\setminus$ $K$ is an open connected set

Evaluating $ \int_0^\pi \frac{\cos{n\theta}}{1 -2r\cos{\theta}+r^2} d\theta $

Show $(\frac{x^n}{n!})'=\frac{x^{n-1}}{(n-1)!}$

complex integral , with singularity ${1\over \pi}$

Harmonic Functions and Partial Derivatives with Chain Rule (Complex Variables)

If $f$ is an entire function such that for each $\theta$, $|f(re^{i\theta})|\rightarrow \infty$ as $r\rightarrow \infty$

Let $\gamma_r(t) = 1+re^{it}$ for $0\leq t \leq \pi/4$. Calculate $\lim\limits_{r\rightarrow 0+} \int_{\gamma_r} \frac{\cos (\pi z)}{\log z}$

Complex polynomial that has no roots in the closed unit disc

If $\int f(z) dz = 0$ for every closed triangular region $T ⊂ U$. Show that $f$ is holomorphic on $U$

Please prove the statement in description given in section 3 of Quantum Mechanics (Landau & Lifshitz).

Complex Analysis : A function satisfying certain conditions , a counterexample?

Find the radius of convergence of Maclaurin series of $(1 + z)^α$

Evaluating the Laurent series of $\frac{1}{\exp (z) -1 }$

Finding the singularities of a complex function.

If $f_1,...,f_k$ are given holomorphic functions and $f$ is such that $f_i/f$ is holomorphic then $g_1f_1 + \cdots + g_nf_n = gf$

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