List questions from beta-function

Published on 04 Aug 2021 - 9:27

196

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Show that for a fixed $q$ the Beta function $B(p,q)$ is log convex.

Published on 15 Aug 2021 - 20:33

402

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Intuition of Beta distribution with less-than-one parameters

Published on 08 Sep 2021 - 9:08

188

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A series expansion for $\left(x^2\,B(x,x)\right)^\frac nx$ or $\frac{1}{(Γ(2x))^\frac nx}$ for $0\lt x\le 1, n\in\Bbb N$

Published on 10 Sep 2021 - 2:32

287

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Is there an integral representation of the multivariate beta function?

Published on 12 Sep 2021 - 10:02

100

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Difference between finding asymptotics of Beta function through Laplace versus through Stirling

Published on 26 Mar 2026 - 6:20

103

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Closed form of beta distribution CDF when $\alpha + \beta = 1$

Published on 14 Sep 2021 - 2:30

457

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Surface area of n-dim hyperspherical cap idea

Published on 25 Mar 2026 - 14:39

171

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I have a question about combination series. i don't understand that

Published on 11 Oct 2021 - 10:42

459

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How to evaluate the integral $I = \int_o^{\infty} \frac{x}{\sqrt{e^{2\pi\sqrt{x}}-1}}dx$?

Published on 30 Oct 2021 - 19:21

175

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Integral similar to Beta function

Published on 17 Nov 2021 - 7:53

86

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Simplifying $\int_0^1 x^{a-1} (1-x)^{b-1} \, _2F_1\left(1,d;c+d+1;2-\frac{1}{x}\right) \, dx$

Published on 22 Nov 2021 - 17:08

373

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Derive Stirling's Approximation for Beta Function

Published on 25 Nov 2021 - 23:59

112

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Baby rudin 8.21

Published on 26 Nov 2021 - 15:25

116

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Question on Rudin's exercise 8.21

Published on 27 Nov 2021 - 13:46

List Question

Good Lower bound on the Beta function

Show that for a fixed $q$ the Beta function $B(p,q)$ is log convex.

Intuition of Beta distribution with less-than-one parameters

A series expansion for $\left(x^2\,B(x,x)\right)^\frac nx$ or $\frac{1}{(Γ(2x))^\frac nx}$ for $0\lt x\le 1, n\in\Bbb N$

Is there an integral representation of the multivariate beta function?

Difference between finding asymptotics of Beta function through Laplace versus through Stirling

Closed form of beta distribution CDF when $\alpha + \beta = 1$

Surface area of n-dim hyperspherical cap idea

I have a question about combination series. i don't understand that

How to evaluate the integral $I = \int_o^{\infty} \frac{x}{\sqrt{e^{2\pi\sqrt{x}}-1}}dx$?

Integral similar to Beta function

Simplifying $\int_0^1 x^{a-1} (1-x)^{b-1} \, _2F_1\left(1,d;c+d+1;2-\frac{1}{x}\right) \, dx$

Derive Stirling's Approximation for Beta Function

Baby rudin 8.21

Question on Rudin's exercise 8.21

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