List questions from beta-function

52

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Relation of distribution of $\frac{X}{X+Y}$ where $X,Y$ are iid. rv s.t exponential distribution and parameter $\alpha>0$ and $\beta'(\alpha,\alpha)$.

Published on 27 Mar 2026 - 13:48

114

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Completing the explicit $\lim\limits_{c\to0}\text I^{-1}_{cx}(r,c)$/ inverse $\int_0^x\frac{t^{r-1}}{1-t}dt,r\in\Bbb Q$ series expansion

Published on 24 Feb 2026 - 8:34

374

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Seeking for other methods to evaluate $\int_0^{\infty} \frac{\ln \left(x^n+1\right)}{x^n+1} dx$ for $n\geq 2$.

Published on 26 Mar 2026 - 7:35

53

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Chainging the hypergeometric series $F(\alpha,\beta,\gamma;z)$ to an integral form

Published on 16 Nov 2022 - 12:41

193

Views

Weierstrass Zeta $\zeta(x;a,b)$ inverse

Published on 28 Mar 2026 - 3:34

87

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How to simplify RMM limit of integral?

Published on 26 Nov 2022 - 3:16

64

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Relation between beta and gamma function by an elementary method :

Published on 26 Nov 2022 - 4:45

99

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Reduction of $_3\text F_2(a,a,1-b;a+1,a+1;x)$ with the hypergeometric function

Published on 04 Dec 2022 - 0:14

119

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$I(a,b)=\int_a^bx^n(x-a)^{-1/2}(b-x)^{-1/2}dx$

Published on 11 Dec 2022 - 15:24

254

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Evaluate $\int_0^\infty\frac{\sqrt[5]{x}}{(x^2+1)(x+1)^2}dx$ using Gamma and Beta functions

Published on 18 Dec 2022 - 14:51

164

Views

Beta function integral convergence?

Published on 08 Jan 2023 - 7:21

55

Views

Prove $B(a,\frac{1}{2}) \ge \frac{1}{a}$ for $a \ge 1$

Published on 16 Jan 2023 - 8:44

List Question

Relation of distribution of $\frac{X}{X+Y}$ where $X,Y$ are iid. rv s.t exponential distribution and parameter $\alpha>0$ and $\beta'(\alpha,\alpha)$.

Completing the explicit $\lim\limits_{c\to0}\text I^{-1}_{cx}(r,c)$/ inverse $\int_0^x\frac{t^{r-1}}{1-t}dt,r\in\Bbb Q$ series expansion

Seeking for other methods to evaluate $\int_0^{\infty} \frac{\ln \left(x^n+1\right)}{x^n+1} dx$ for $n\geq 2$.

Chainging the hypergeometric series $F(\alpha,\beta,\gamma;z)$ to an integral form

Weierstrass Zeta $\zeta(x;a,b)$ inverse

How to simplify RMM limit of integral?

Relation between beta and gamma function by an elementary method :

Reduction of $_3\text F_2(a,a,1-b;a+1,a+1;x)$ with the hypergeometric function

$I(a,b)=\int_a^bx^n(x-a)^{-1/2}(b-x)^{-1/2}dx$

Evaluate $\int_0^\infty\frac{\sqrt[5]{x}}{(x^2+1)(x+1)^2}dx$ using Gamma and Beta functions

Beta function integral convergence?

Prove $B(a,\frac{1}{2}) \ge \frac{1}{a}$ for $a \ge 1$

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