Question

Prove $\frac{\partial}{\partial m}\text{B}(n,m)=-\text{B}(n,m)\sum_{k=0}^{n-1}\frac{1}{k+m}$

score 581 · Answer 1 · 2019-06-16 05:00:13

581

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Prove $\frac{\partial}{\partial m}\text{B}(n,m)=-\text{B}(n,m)\sum_{k=0}^{n-1}\frac{1}{k+m}$

Published on 16 Jun 2019 - 5:00

score 99 · Answer 2 · 2019-06-18 00:35:26

99

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SImplification of $I=\int_{x=0}^{\infty}x^{n-1}(\alpha-x)^{m}e^{-\mu x}dx.$

Published on 18 Jun 2019 - 0:35

score 33 · Answer 3 · 2019-06-21 09:17:41

33

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How to calculate the variance

Published on 21 Jun 2019 - 9:17

score 182 · Answer 4 · 2019-06-29 12:27:44

182

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Prove that : $\int_0^{1}\frac{1-\sqrt{1-x^{4}}}{x^{2}\sqrt{1-x^4}}dx=1-\frac{\sqrt{2}\pi^{\frac{3}{2}}}{\Gamma(\frac{1}{4})^2}$

Published on 29 Jun 2019 - 12:27

score 97 · Answer 5 · 2026-03-25 07:47:23

97

Views

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score 79 · Answer 6 · 2019-07-12 07:18:56

79

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score 605 · Answer 7 · 2019-07-16 04:58:27

605

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$ \int_0^\frac{\pi}{2}\ln^n\left(\tan(x)\right)\:dx$

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score 36 · Answer 8 · 2026-03-25 09:50:18

36

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Show that $\int_{0}^{1}\left[\frac{I\left(x,n,N-n\right)-I\left(x,n,N-n\right)}{1-2n/N}\right]^{2}dx$ is increasing in $n$?

Published on 25 Mar 2026 - 9:50

score 177 · Answer 9 · 2019-08-09 14:46:48

177

Views

Finding conditional probability of "success" when success probability is random

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score 144 · Answer 10 · 2019-08-22 12:24:47

144

Views

A special integral related to Beta function

Published on 22 Aug 2019 - 12:24

score 300 · Answer 11 · 2026-03-25 11:03:43

300

Views

Find the closed form of $\sum\limits_{k=0}^n \frac{1}{n\choose k}$: Incomplete Beta function in a combinatoric question

Published on 25 Mar 2026 - 11:03

score 79 · Answer 12 · 2019-09-05 15:10:55

79

Views

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score 138 · Answer 13 · 2019-09-16 21:17:31

138

Views

Product of two Gamma Functions: munging two integrals together with variable change to obtain result

Published on 16 Sep 2019 - 21:17

score 209 · Answer 14 · 2019-09-18 13:38:27

209

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Integral $\int_{-1}^{1}\ln\left(\frac{1+x}{1-x}\right)\frac{\mathrm dx}{(1-x)^{2/3}(1+x)^{1/3}} $

Published on 18 Sep 2019 - 13:38

score 310 · Answer 15 · 2019-09-18 14:47:03

310

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Integral $\int_{0}^{\pi}\frac{\sin^px}{1+\cos x} dx $

Published on 18 Sep 2019 - 14:47

List Question

Prove $\frac{\partial}{\partial m}\text{B}(n,m)=-\text{B}(n,m)\sum_{k=0}^{n-1}\frac{1}{k+m}$

SImplification of $I=\int_{x=0}^{\infty}x^{n-1}(\alpha-x)^{m}e^{-\mu x}dx.$

How to calculate the variance

Prove that : $\int_0^{1}\frac{1-\sqrt{1-x^{4}}}{x^{2}\sqrt{1-x^4}}dx=1-\frac{\sqrt{2}\pi^{\frac{3}{2}}}{\Gamma(\frac{1}{4})^2}$

Solving an integral with limits of polygamma functions

Maclaurin expansion for $~x^a~(1-x)^b~$

$ \int_0^\frac{\pi}{2}\ln^n\left(\tan(x)\right)\:dx$

Show that $\int_{0}^{1}\left[\frac{I\left(x,n,N-n\right)-I\left(x,n,N-n\right)}{1-2n/N}\right]^{2}dx$ is increasing in $n$?

Finding conditional probability of "success" when success probability is random

A special integral related to Beta function

Find the closed form of $\sum\limits_{k=0}^n \frac{1}{n\choose k}$: Incomplete Beta function in a combinatoric question

Find this integration with conditions

Product of two Gamma Functions: munging two integrals together with variable change to obtain result

Integral $\int_{-1}^{1}\ln\left(\frac{1+x}{1-x}\right)\frac{\mathrm dx}{(1-x)^{2/3}(1+x)^{1/3}} $

Integral $\int_{0}^{\pi}\frac{\sin^px}{1+\cos x} dx $

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