Question

How do I compute the integral $\int\limits_0^1 t^a(1/2 - t)^b\ dt$?

score 76 · Answer 1 · 2022-04-03 00:16:07

76

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How do I compute the integral $\int\limits_0^1 t^a(1/2 - t)^b\ dt$?

Published on 03 Apr 2022 - 0:16

score 211 · Answer 2 · 2022-04-03 07:07:29

211

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How to evaluate $\sum_{k=1}^{\infty}\frac{B\left(k, \frac{1}{2}\right)}{(2k+1)^2}$, where $B(x, y)$ is the Beta function?

Published on 03 Apr 2022 - 7:07

score 88 · Answer 3 · 2026-03-28 02:04:36

88

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calculating weekly occupancy given daily capacity and booking

Published on 28 Mar 2026 - 2:04

score 129 · Answer 4 · 2022-04-03 21:57:09

129

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Integral involving beta function (continuous version of binomial distribution)

Published on 03 Apr 2022 - 21:57

score 107 · Answer 5 · 2022-04-08 21:44:52

107

Views

evaluate integral using beta function

Published on 08 Apr 2022 - 21:44

score 66 · Answer 6 · 2022-04-12 09:08:10

66

Views

Computing ratio $ \frac{\int_{0}^{1}\left(1-x^{k}\right)^{n} d x}{\int_{0}^{1}\left(1-x^{k}\right)^{n+1}dx} $ by other means than Beta integrals

Published on 12 Apr 2022 - 9:08

score 66 · Answer 7 · 2022-04-15 18:30:44

66

Views

An integral inside an integral turns into a product of two integrals?

Published on 15 Apr 2022 - 18:30

score 117 · Answer 8 · 2022-04-20 11:10:58

117

Views

Solution to this hypergeometric function-beta function product integral

Published on 20 Apr 2022 - 11:10

score 84 · Answer 9 · 2022-04-20 14:54:07

84

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Solution to this beta function integral-within-an-integral (Continued)

Published on 20 Apr 2022 - 14:54

score 73 · Answer 10 · 2022-04-21 12:53:03

73

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Calculate $\int_0^{\infty}y^{-\frac{1}{2}}(1+y)^{-m}dy$

Published on 21 Apr 2022 - 12:53

score 275 · Answer 11 · 2026-03-28 06:01:02

275

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Does the Incomplete Beta function have forms of Elliptic E besides $\frac14 \text B_{\sin^2(2x)}\left(\frac12,\frac34\right)=\text E(x,2)$?

Published on 28 Mar 2026 - 6:01

score 95 · Answer 12 · 2022-05-02 11:00:58

95

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Under which circumstances is the incomplete beta function equal to Gauss hypergeometric function

Published on 02 May 2022 - 11:00

score 55 · Answer 13 · 2022-05-06 02:05:41

55

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A Regularized Beta function limit: $\lim_{a\to0}\frac{1-\text I_\frac zb(a,b)}a$

Published on 06 May 2022 - 2:05

score 34 · Answer 14 · 2022-05-23 17:21:38

34

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how to find the table integral that contains factorial of n?

Published on 23 May 2022 - 17:21

score 116 · Answer 15 · 2022-05-30 16:56:25

116

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The integral $\int_{0}^{\pi/2} \tan^p x~dx$

Published on 30 May 2022 - 16:56

List Question

How do I compute the integral $\int\limits_0^1 t^a(1/2 - t)^b\ dt$?

How to evaluate $\sum_{k=1}^{\infty}\frac{B\left(k, \frac{1}{2}\right)}{(2k+1)^2}$, where $B(x, y)$ is the Beta function?

calculating weekly occupancy given daily capacity and booking

Integral involving beta function (continuous version of binomial distribution)

evaluate integral using beta function

Computing ratio $ \frac{\int_{0}^{1}\left(1-x^{k}\right)^{n} d x}{\int_{0}^{1}\left(1-x^{k}\right)^{n+1}dx} $ by other means than Beta integrals

An integral inside an integral turns into a product of two integrals?

Solution to this hypergeometric function-beta function product integral

Solution to this beta function integral-within-an-integral (Continued)

Calculate $\int_0^{\infty}y^{-\frac{1}{2}}(1+y)^{-m}dy$

Does the Incomplete Beta function have forms of Elliptic E besides $\frac14 \text B_{\sin^2(2x)}\left(\frac12,\frac34\right)=\text E(x,2)$?

Under which circumstances is the incomplete beta function equal to Gauss hypergeometric function

A Regularized Beta function limit: $\lim_{a\to0}\frac{1-\text I_\frac zb(a,b)}a$

how to find the table integral that contains factorial of n?

The integral $\int_{0}^{\pi/2} \tan^p x~dx$

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