User Random Variable - Mathematics Stack Exchange

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1

17

votes

1

answer

524

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when a real-valued integral can't be evaluated using contour integration

complex-analysis integral

may 30 '12 at 2:01 rotskoff 206

2

12

votes

1

answer

182

views

$\prod_{n=2}^{\infty}\left(1-\frac{1}{n^3}\right)$

mar 4 at 4:19 Random Variable 1,671

1

8

votes

3

answers

179

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Evaluating $\sum_{n=1}^{\infty} \frac{n}{e^{2 \pi n}-1}$ using the inverse Mellin transform

sequences-and-series complex-analysis

2d ago Marko Riedel 1,879

1

7

votes

1

answer

90

views

Evaluating $\int_{0}^{\infty}\Big( \frac{x^{a-1}}{\sinh x} - x^{a-2} \Big) \ dx$

complex-analysis definite-integral

may 10 at 0:45 Random Variable 1,671

1

7

votes

1

answer

139

views

integral with hyperbolic cosines

complex-analysis integral

jan 30 at 11:10 Ron Gordon 26.4k

6

votes

1

answer

97

views

Can you integrate near some essential singularities?

complex-analysis

apr 7 at 18:09 robjohn♦ 59.6k

6

votes

1

answer

84

views

determining if a complex number is a root of unity

algebra-precalculus complex-numbers

jan 30 at 17:03 Michael Hardy 48.1k

3

6

votes

1

answer

191

views

improper integral with an absolute value

complex-analysis integral

jan 24 at 18:23 Sasha 41.4k

5

votes

3

answers

80

views

Evaluating $ \int_{-\infty}^{\infty} \frac{\cos \left(x-\frac{1}{x} \right)}{1+x^{2}} \ dx$

complex-analysis integration contour-integration

apr 18 at 19:23 Sharkos 4,515

1

5

votes

1

answer

96

views

integral involving the Beta function

real-analysis integral

mar 2 at 21:51 Coiacy 515

5

votes

1

answer

402

views

bringing a limit inside of an integral

real-analysis limit integration

mar 19 '12 at 22:37 Community♦ 1

4

votes

1

answer

81

views

Evaluating $\int_{0}^{\infty} \frac{2 \cos x \ln x + \pi \sin x}{x^2+4} \ dx$

complex-analysis contour-integration

apr 25 at 0:19 Sharkos 4,515

4

votes

2

answers

78

views

Integrating by substitution

calculus integral integration definite-integral

apr 5 at 4:35 Random Variable 1,671

4

votes

2

answers

62

views

branch cuts of the logarithm

complex-analysis

mar 14 at 0:00 paul garrett 10.5k

4

votes

1

answer

109

views

Integrals of functions related to the sinc function

complex-analysis integral

mar 8 at 22:17 Random Variable 1,671

4

votes

1

answer

93

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a couple of Fresnel-like integrals

complex-analysis integral

feb 22 at 13:27 Ron Gordon 26.4k

2

4

votes

0

answers

55

views

adding a second parameter to an integral

complex-analysis integral

feb 20 at 22:13 Random Variable 1,671

2

4

votes

2

answers

414

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evaluating a real-valued integral using contour integration and the residue at infinity

complex-analysis integral

mar 25 '12 at 21:07 Robert Israel 86.4k

3

votes

1

answer

31

views

The partial fraction decomposition of $\frac{x^{2m-1}}{\prod_{k=1}^{n} (x^{2}+k^{2})}$

calculus partial-fractions

apr 21 at 2:27 vonbrand 6,568

3

votes

0

answers

84

views

contour integration around a dogbone/dumbbell contour

complex-analysis contour-integration

apr 6 at 18:52 Random Variable 1,671

3

votes

3

answers

173

views

functions with multiple branch points

complex-analysis

mar 14 at 0:38 paul garrett 10.5k

1

3

votes

1

answer

100

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Cauchy principal value of $\int_{-\infty}^{\infty} \frac{1}{x^{3}} \ dx $

complex-analysis contour-integration

mar 6 at 23:33 mrf 8,422

3

votes

1

answer

68

views

contour integration of $f(z) = z^{a-1}(z+z^{-1})^{b-1}$

complex-analysis contour-integration

mar 5 at 21:04 Ron Gordon 26.4k

3

votes

1

answer

469

views

Show $\int_{-\infty}^{\infty} \frac{\sinh ax}{\sinh \pi z} \cos bx \ dx = \frac{\sin a}{\cos a + \cosh b} \ -\pi < a < \pi$

complex-analysis integral

oct 10 at 17:02 Community♦ 1

3

votes

1

answer

275

views

summation of an infinite series involving arctan

sequences-and-series complex-analysis logarithms branch-cuts

apr 5 '12 at 5:29 alex.jordan 8,814

2

votes

1

answer

67

views

Behavior of $\Gamma(z)$ as $\text{Im} (z) \to \pm \infty$

complex-numbers asymptotics gamma-function

18h ago A Walker 2,281

2

votes

2

answers

56

views

Laplace transform of the derivative of the Dirac delta function

laplace-transform weak-derivatives

may 1 at 0:34 fgp 4,839

2

votes

2

answers

106

views

Summation of series using residues

complex-analysis contour-integration residue-calculus

apr 13 at 20:40 Marko Riedel 1,879

1

2

votes

1

answer

151

views

Inverse Laplace transform using contour integration

complex-analysis laplace-transform contour-integration

apr 3 at 20:55 Random Variable 1,671

2

votes

1

answer

86

views

analytic continuation

complex-analysis

mar 23 at 12:02 julien 22.7k

Random Variable

52 Questions