User arbautjc - Mathematics Stack Exchange

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	location	Besancon, France
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stats	profile views	189

	815 reputation	bio	website		visits	member for	7 months
113 badges		location	Besancon, France		seen	yesterday

9

16

votes

1

answer

180

views

$\int_0^1\arctan\,_4F_3\left(\frac{1}{5},\frac{2}{5},\frac{3}{5},\frac{4}{5};\frac{1}{2},\frac{3}{4},\frac{5}{4};\frac{x}{64}\right)\,\mathrm dx$

may 17 at 5:30 Laila Podlesny 806

4

8

votes

1

answer

145

views

The series $\sum_{n=1}^\infty \frac{(-1)^{n+1}}{2n-1}\mbox{sech}\left(\frac{(2n-1)\pi}{2}\right)$

sequences-and-series complex-analysis analysis special-functions

apr 14 at 17:59 Argon 9,276

4

9

votes

1

answer

140

views

Evaluate $\int _{ 0 }^{ 1 }{ \left( { x }^{ 5 }+{ x }^{ 4 }+{ x }^{ 2 } \right) \sqrt { 4{ x }^{ 3 }+5{ x }^{ 2 }+10 } \; dx } $

calculus integral definite-integral

apr 13 at 18:44 jdh8 83

2

9

votes

3

answers

140

views

Evaluating $\lim \limits_{n\to \infty} \left( n \int_{0}^{\frac \pi 2} 1-\sqrt [n]{\sin x} \,\mathrm dx \right)$

calculus sequences-and-series limit integration convergence

apr 11 at 15:50 Ishan Banerjee 3,752

5

votes

4

answers

328

views

Evaluating $\int_0^{\infty}\frac{\ln(x^2+1)}{x^2+1}dx$

complex-analysis integral integration logarithms contour-integration

apr 24 at 14:17 Ron Gordon 26.7k

1

4

votes

3

answers

79

views

Integral with Bessel functions of the First Kind.

integration special-functions definite-integral

apr 11 at 19:04 arbautjc 815

1

5

votes

1

answer

71

views

Prove that $\lim_{t \rightarrow 0} t \int_{0}^{\infty} e^{-tx} f(x) dx =1$

analysis limit integration

apr 10 at 7:04 mikefallopian 83

2

7

votes

2

answers

112

views

How to integrate $f( \theta ) = \frac{1}{a + \sin( \theta ) }$?

homework complex-analysis

apr 9 at 14:12 xpaul 1,056

1

8

votes

3

answers

105

views

How to prove $\cos\left(\pi\over7\right)-\cos\left({2\pi}\over7\right)+\cos\left({3\pi}\over7\right)=\cos\left({\pi}\over3 \right)$

geometry trigonometry

mar 31 at 9:53 Ben 553

9

15

votes

2

answers

240

views

How to find the value of $\sin{\dfrac{\pi}{14}}+6\sin^2{\dfrac{\pi}{14}}-8\sin^4{\dfrac{\pi}{14}}$

trigonometry

apr 18 at 13:59 TMM 7,156

1

2

votes

1

answer

49

views

Show $z\to\frac{2}{1-z}$ sends unit semicircle to $x=1$ and line $x=1$ to $x=0$

geometry complex-analysis

mar 30 at 17:32 Martin Brandenburg 23.1k

6

10

votes

1

answer

268

views

How to prove $\int_{0}^{\pi}\frac{\sin^n{x}}{(1+r^2-2r\cos{x})^{(n+2)/2}}\,\mathrm dx=\frac{1}{1-r^2}\int_{0}^{\pi}\sin^n{x}\,\mathrm dx$

integral definite-integral

1d ago user64494 375

1

3

votes

1

answer

138

views

How is the formula for the focal point of a ball lens derived?

trigonometry physics analytic-geometry

mar 29 at 12:31 DarkLightA 147

1

3

votes

3

answers

104

views

ln and rational function using contour integration

contour-integration

mar 30 at 15:00 Cody 2,613

4

votes

2

answers

86

views

Series involving factorials

sequences-and-series factorial

mar 29 at 8:16 Gautam Shenoy 2,309

2

6

votes

2

answers

92

views

Show that $\frac{\sin x}{\cos 3x}+\frac{\sin 3x}{\cos 9x}+\frac{\sin 9x}{\cos 27x} = \frac{1}{2}\left(\tan 27x-\tan x\right)$

trigonometry

apr 1 at 7:47 Adi Dani 6,007

1

3

votes

2

answers

74

views

If $(\pm x)^2 = X$ then $\sqrt{X} = x$?

algebra-precalculus

mar 27 at 16:52 Kaish 1,818

2

11

votes

1

answer

156

views

How to prove this inequality(7)?

inequality

1d ago user64494 375

1

3

votes

2

answers

71

views

$\sin{\frac{A+B}{2}}+\sin{\frac{B+C}{2}}+\sin{\frac{C+A}{2}} > \sin{A}+\sin{B}+\sin{C}. $

geometry trigonometry

mar 27 at 9:09 Easy 2,615

2

3

votes

2

answers

104

views

Integral inequality: $\dfrac{1}{30}<\int_{2}^{\infty}\dfrac{\sqrt{s^3-s^2+3}}{s^5+s^2+1}ds<\dfrac{\sqrt{2}}{20}$

integral

mar 27 at 13:18 Christian Blatter 32.7k

1

3

votes

3

answers

154

views

Why can't $\pi$ be expressed as a fraction?

pi

mar 26 at 9:39 Christian Blatter 32.7k

3

15

votes

1

answer

187

views

References to integrals of the form $\int_{0}^{1} \left( \frac{1}{\log x}+\frac{1}{1-x} \right)^{m} \, dx$

integral reference-request riemann-zeta

mar 27 at 10:55 sos440 14.5k

2

9

votes

2

answers

276

views

Evaluate the integral $\int_0^{\infty} \left(\frac{\log x \arctan x}{x}\right)^2 \ dx$

calculus integral

mar 25 at 2:04 Mhenni Benghorbal 14.2k

1

5

votes

1

answer

66

views

finding $\lim_{n\rightarrow\infty}\sum_{r=1}^{n}\arctan\left(\frac{2r}{1-r^2+r^4}\right)$

sequences-and-series trigonometry trigonometric-series

mar 24 at 13:53 DonAntonio 47.3k

3

4

votes

1

answer

106

views

Irreducibility of an infinite sequence of polynomials

irreducible-polynomials

mar 19 at 19:05 P.. 8,935

2

7

votes

3

answers

198

views

Value of $\sum_{k=1}^{\infty}\frac{1}{k^2+a^2}$

real-analysis sequences-and-series

feb 26 at 19:00 Cortizol 1,316

3

13

votes

2

answers

277

views

Evaluation of $\int_0^{\pi/3} \ln^2\left(\frac{\sin x }{\sin (x+\pi/3)}\right)\,\mathrm{d}x$

calculus real-analysis definite-integral contour-integration residue-calculus

mar 11 at 15:59 Ron Gordon 26.7k

1

3

votes

2

answers

271

views

Laurent series expansion of $f(z)=\frac{1}{(z-1)^2(z+1)^2}$

complex-analysis laurent-series

mar 29 at 7:58 Martin 3,780

4

8

votes

1

answer

1

kviews

A hard definite integral with trignometric

calculus sequences-and-series integral trigonometry

jan 26 at 7:30 Ron Gordon 26.7k

2

8

votes

2

answers

405

views

can $ \int_0^{\pi/2} \ln ( \sin(x)) \; dx$ be evaluated with complex integral

complex-analysis

sep 3 at 14:47 kiwi 401

arbautjc

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