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Integral using gamma and beta functions

score 489 · Answer 1 · 2015-06-20 09:57:26

489

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Integral using gamma and beta functions

Published on 20 Jun 2015 - 9:57

score 1.2k · Answer 2 · 2015-07-09 19:13:01

1.2k

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Difference of Ordered Uniform Random Variables

Published on 09 Jul 2015 - 19:13

score 182 · Answer 3 · 2015-07-14 05:40:38

182

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Beta-gamma integrals

Published on 14 Jul 2015 - 5:40

score 56 · Answer 4 · 2026-03-25 19:04:36

56

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Infrequent fail of the popular parameter estimators, having several beta-distributed random variables to be estimated

Published on 25 Mar 2026 - 19:04

score 242 · Answer 5 · 2015-07-30 00:17:32

242

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An Infinite series I

Published on 30 Jul 2015 - 0:17

score 2.5k · Answer 6 · 2015-08-06 01:50:18

2.5k

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Beta Distribution and Expectation and Variance

Published on 06 Aug 2015 - 1:50

score 667 · Answer 7 · 2015-09-02 07:30:34

667

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Evaluating $~\int_0^1\sqrt{\frac{1+x^n}{1-x^n}}~dx~$ and $~\int_0^1\sqrt[n]{\frac{1+x^2}{1-x^2}}~dx$

Published on 02 Sep 2015 - 7:30

score 996 · Answer 8 · 2015-09-06 10:48:57

996

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If $ I = \int_{0}^{1}\left[1-(1-x^2)^{100}\right]^{201} xdx$ and $J=\int_{0}^{1}\left[1-(1-x^2)^{100}\right]^{202}xdx\;,$ Then $ \frac{I}{J}$

Published on 06 Sep 2015 - 10:48

score 642 · Answer 9 · 2015-09-10 00:16:42

642

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How to derive Clopper-Pearson interval's F and beta approximation?

Published on 10 Sep 2015 - 0:16

score 90 · Answer 10 · 2015-09-14 08:08:16

90

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How to prove the summation $\sum\limits_{i=0}^b {b \choose i}(-1)^i\frac{1}{a+i+1}=\frac{a!b!}{(a+b+1)!}$

Published on 14 Sep 2015 - 8:08

score 2.4k · Answer 11 · 2015-09-24 16:25:59

2.4k

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Beta distribution times a scalar

Published on 24 Sep 2015 - 16:25

score 63 · Answer 12 · 2015-09-25 15:11:09

$\lim_{\alpha\rightarrow 0}\left(\alpha^{(m+1)/m-2/n}\int_0^{\tan^{-1}(\alpha^{-1})}\sin^{1/m}(\theta)\cos^{2(1-n)n-1/m}(\theta)\:d\theta\right)=$?

score 91 · Answer 13 · 2015-09-28 09:35:58

91

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finding the closed-form of $k$ in the series $\sum_{n=1}^{m}\beta (2n-1)\zeta (2n)=m+k$

Published on 28 Sep 2015 - 9:35

score 112 · Answer 14 · 2015-09-29 05:27:10

112

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Proving that: $\int_0^{\infty}{\dfrac{\cosh(2yt)}{(\cosh(t))^{2x}}dt}=2^{2x-2}\cdot\dfrac{\Gamma(x+y)\Gamma(x-y)}{\Gamma(2x)}$

Published on 29 Sep 2015 - 5:27

score 1k · Answer 15 · 2026-03-18 23:54:00

1k

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kth Moment of Beta Distribution

Published on 18 Mar 2026 - 23:54

List Question

Integral using gamma and beta functions

Difference of Ordered Uniform Random Variables

Beta-gamma integrals

Infrequent fail of the popular parameter estimators, having several beta-distributed random variables to be estimated

An Infinite series I

Beta Distribution and Expectation and Variance

Evaluating $~\int_0^1\sqrt{\frac{1+x^n}{1-x^n}}~dx~$ and $~\int_0^1\sqrt[n]{\frac{1+x^2}{1-x^2}}~dx$

If $ I = \int_{0}^{1}\left[1-(1-x^2)^{100}\right]^{201} xdx$ and $J=\int_{0}^{1}\left[1-(1-x^2)^{100}\right]^{202}xdx\;,$ Then $ \frac{I}{J}$

How to derive Clopper-Pearson interval's F and beta approximation?

How to prove the summation $\sum\limits_{i=0}^b {b \choose i}(-1)^i\frac{1}{a+i+1}=\frac{a!b!}{(a+b+1)!}$

Beta distribution times a scalar

$\lim_{\alpha\rightarrow 0}\left(\alpha^{(m+1)/m-2/n}\int_0^{\tan^{-1}(\alpha^{-1})}\sin^{1/m}(\theta)\cos^{2(1-n)n-1/m}(\theta)\:d\theta\right)=$?

finding the closed-form of $k$ in the series $\sum_{n=1}^{m}\beta (2n-1)\zeta (2n)=m+k$

Proving that: $\int_0^{\infty}{\dfrac{\cosh(2yt)}{(\cosh(t))^{2x}}dt}=2^{2x-2}\cdot\dfrac{\Gamma(x+y)\Gamma(x-y)}{\Gamma(2x)}$

kth Moment of Beta Distribution

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