User dcholleton

3 votes

2 answers

39k views

How to show $\sin(x+iy)=\sin(x) \cosh(y) + i\cos(x) \sinh(y)$

asked Apr 14, 2014 at 9:25

3 votes

0 answers

238 views

Is there a simple and fast way of computing the residue at an essential singularity?

asked Apr 14, 2014 at 10:16

3 votes

3 answers

82 views

How to prove that $ \sum_{n=0}^\infty \frac{1}{(2n+1)^2} + \sum_{k=1}^\infty \frac{1}{(2k)^2}=\frac{4}{3} \sum_{n=0}^\infty \frac{1}{(2n+1)^2}$

asked May 31, 2014 at 14:16

2 votes

1 answer

773 views

How to compute residue of $f(z)=z^3e^{\frac{1}{z}}$?

asked May 29, 2014 at 21:33

2 votes

1 answer

150 views

I want to compute $\int_0^\infty \frac{x^t}{1+x^2}dx \; \forall t \in (-1,1)$ using residue theroem.

asked Apr 14, 2014 at 16:23

2 votes

1 answer

116 views

How to solve $\ddot z + Az = 0$

asked Sep 17, 2015 at 21:02

1 vote

3 answers

135 views

How to prove $ z^n - z^n_0 = (z-z_0) \sum_0^{n-1} z^kz_0^{n-1-k} $ [duplicate]

asked Apr 13, 2014 at 19:15

1 vote

1 answer

87 views

How to prove that $\pi \frac{e^{it\frac{\pi}{2}}-e^{it\frac{3\pi}{2}}}{1 - e^{2\pi it}} = \frac{\pi}{2\cos\left(\frac{\pi t}{2}\right)}$

asked Apr 15, 2014 at 13:41

1 vote

1 answer

85 views

Deducing Laplace Formulas

asked Apr 16, 2014 at 11:49

1 vote

0 answers

90 views

How to find poles and singularities of $f(z) = \frac{\text {ln}(1+z)}{z(e^{iz}-1)} $

asked May 29, 2014 at 23:41

1 vote

2 answers

48 views

Proving continuity of $f(x) = \sum_{n=0}^\infty \frac{1}{1+x^n} \quad x\in\;]1,\infty[$

asked Dec 16, 2014 at 23:03

1 vote

0 answers

32 views

How to show $ \text{Re}f(x) = \frac{1}{\pi} \mathcal{P} \int_{-\infty}^\infty \frac{\text{Im}f(x')}{x'-x}dx' $

asked May 31, 2014 at 18:57

1 vote

0 answers

14 views

How to prove $ \mathcal{P}\int_{-\infty}^\infty \frac{\text{Im}f(x')}{x'-x} = \mathcal{P}\int_{-\infty}^\infty \frac{x'\text{Im}f(x')}{x'^2-x^2} $

asked May 31, 2014 at 22:17

0 votes

1 answer

65 views

How to prove that $ \ln(1-e^{-x})=\sum_{k=0}^\infty \frac{e^{-kx}}{k}$ if $x>0$ [closed]

asked Jun 4, 2014 at 23:02

0 votes

1 answer

80 views

How to compute the Laurent series for $f(z) = \frac{z+i}{z-i} $

asked Jun 7, 2014 at 15:10

0 votes

1 answer

45 views

How to compute this series

asked Dec 17, 2014 at 9:02

0 votes

1 answer

32 views

Series convergence issues

asked Dec 17, 2014 at 10:02

0 votes

1 answer

28 views

How to know that $(z-z_0^3)(z-z_0^5)(z-z_0^7) = \sum_{k=0}^3 z^k z^{3-k}_0$

asked Apr 16, 2014 at 13:28

0 votes

1 answer

72 views

How to compute this integral : $\oint \bar{z}^n dz$

asked Apr 12, 2014 at 11:22

0 votes

2 answers

33 views

How to compute $f(z) = \sum_0^{\infty} (1+2i+(2+i)(-1)^k)^{-k}z^k$

asked Apr 13, 2014 at 14:25

0 votes

1 answer

35 views

Is $\sum_0^\infty (-1)^k z^{k-1}$ equal to $\sum_{-1}^\infty (-1)^{k+1} z^{k}$

asked Apr 13, 2014 at 16:13

0 votes

3 answers

35 views

How to find the $n$ zeros of $\displaystyle1+z^n$?

asked Apr 13, 2014 at 17:27

Stack Exchange Network

22 Questions

How to show $\sin(x+iy)=\sin(x) \cosh(y) + i\cos(x) \sinh(y)$

Is there a simple and fast way of computing the residue at an essential singularity?

How to prove that $ \sum_{n=0}^\infty \frac{1}{(2n+1)^2} + \sum_{k=1}^\infty \frac{1}{(2k)^2}=\frac{4}{3} \sum_{n=0}^\infty \frac{1}{(2n+1)^2}$

How to compute residue of $f(z)=z^3e^{\frac{1}{z}}$?

I want to compute $\int_0^\infty \frac{x^t}{1+x^2}dx \; \forall t \in (-1,1)$ using residue theroem.

How to solve $\ddot z + Az = 0$

How to prove $ z^n - z^n_0 = (z-z_0) \sum_0^{n-1} z^kz_0^{n-1-k} $ [duplicate]

How to prove that $\pi \frac{e^{it\frac{\pi}{2}}-e^{it\frac{3\pi}{2}}}{1 - e^{2\pi it}} = \frac{\pi}{2\cos\left(\frac{\pi t}{2}\right)}$

Deducing Laplace Formulas

How to find poles and singularities of $f(z) = \frac{\text {ln}(1+z)}{z(e^{iz}-1)} $

Proving continuity of $f(x) = \sum_{n=0}^\infty \frac{1}{1+x^n} \quad x\in\;]1,\infty[$

How to show $ \text{Re}f(x) = \frac{1}{\pi} \mathcal{P} \int_{-\infty}^\infty \frac{\text{Im}f(x')}{x'-x}dx' $

How to prove $ \mathcal{P}\int_{-\infty}^\infty \frac{\text{Im}f(x')}{x'-x} = \mathcal{P}\int_{-\infty}^\infty \frac{x'\text{Im}f(x')}{x'^2-x^2} $

How to prove that $ \ln(1-e^{-x})=\sum_{k=0}^\infty \frac{e^{-kx}}{k}$ if $x>0$ [closed]

How to compute the Laurent series for $f(z) = \frac{z+i}{z-i} $

How to compute this series

Series convergence issues

How to know that $(z-z_0^3)(z-z_0^5)(z-z_0^7) = \sum_{k=0}^3 z^k z^{3-k}_0$

How to compute this integral : $\oint \bar{z}^n dz$

How to compute $f(z) = \sum_0^{\infty} (1+2i+(2+i)(-1)^k)^{-k}z^k$

Is $\sum_0^\infty (-1)^k z^{k-1}$ equal to $\sum_{-1}^\infty (-1)^{k+1} z^{k}$

How to find the $n$ zeros of $\displaystyle1+z^n$?