Question

An integral related to the beta function: $\int_{-1}^{1} \frac{(1+x)^{2m-1}(1-x)^{2n-1}}{(1+x^{2})^{m+n}} \, dx $

score 856 · Answer 1 · 2013-03-02 19:28:22

856

Views

An integral related to the beta function: $\int_{-1}^{1} \frac{(1+x)^{2m-1}(1-x)^{2n-1}}{(1+x^{2})^{m+n}} \, dx $

Published on 02 Mar 2013 - 19:28

score 71 · Answer 2 · 2020-08-03 17:12:55

71

Views

definite and indefinite integral with hypergeometric function

Published on 03 Aug 2020 - 17:12

score 1.5k · Answer 3 · 2020-08-05 21:20:17

1.5k

Views

Prove: $\int_0^2 \frac{dx}{\sqrt{1+x^3}}=\frac{\Gamma\left(\frac{1}{6}\right)\Gamma\left(\frac{1}{3}\right)}{6\Gamma\left(\frac{1}{2}\right)}$

Published on 05 Aug 2020 - 21:20

score 165 · Answer 4 · 2020-08-05 23:06:46

165

Views

Integral to Gamma function

Published on 05 Aug 2020 - 23:06

score 206 · Answer 5 · 2020-08-18 07:18:01

206

Views

Proving the monotonicity of an implicit function

Published on 18 Aug 2020 - 7:18

score 1.5k · Answer 6 · 2020-08-18 21:49:04

1.5k

Views

Gamma and Beta function proof

Published on 18 Aug 2020 - 21:49

score 186 · Answer 7 · 2026-03-25 23:36:13

186

Views

Evaluating an integral using the beta, gamma and digamma functions

Published on 25 Mar 2026 - 23:36

score 318 · Answer 8 · 2020-08-23 00:08:51

318

Views

Reciprocal of Beta Function

Published on 23 Aug 2020 - 0:08

score 263 · Answer 9 · 2020-08-29 02:43:09

263

Views

What is relationship between beta and binomial distributions in Bayesian inference

Published on 29 Aug 2020 - 2:43

score 131 · Answer 10 · 2020-09-02 17:28:01

131

Views

Compute $\int_0^\infty\frac{x^{2r}}{(1+x^2)^m}\cdot \frac{\Gamma(m)}{\Gamma(1/2)\Gamma(m-1/2)}dx$ using the beta function

Published on 02 Sep 2020 - 17:28

score 141 · Answer 11 · 2020-09-14 08:22:01

141

Views

Value of integral $\int \frac{(1-x)^{n+1}}{x} dx$

Published on 14 Sep 2020 - 8:22

score 99 · Answer 12 · 2026-03-26 06:32:32

99

Views

Uniform rate of convergence of $\sum_{k=0}^{n} {2n+1\choose{k}}\left(a^{k+1}(1-a)^{(2n+1)-k}+a^{(2n+1)-k}(1-a)^{k+1}\right)$ to $\min(a,1-a)$

Published on 26 Mar 2026 - 6:32

score 111 · Answer 13 · 2026-03-26 06:34:47

111

Views

Asymptotic behavior of the CDF of a $\operatorname{Beta}(n,n)$ at $x<1/2$.

Published on 26 Mar 2026 - 6:34

score 158 · Answer 14 · 2020-09-26 07:05:11

158

Views

gamma functions as infinite series

Published on 26 Sep 2020 - 7:05

score 4.1k · Answer 15 · 2020-09-27 22:40:49

4.1k

Views

Computing the value of $\int_0^\frac\pi2\frac{\sin^{2m-1}\theta\cos^{2n-1}\theta}{(a\sin^2\theta+b\cos^2\theta)^{m+n}}\,d\theta$

Published on 27 Sep 2020 - 22:40

List Question

An integral related to the beta function: $\int_{-1}^{1} \frac{(1+x)^{2m-1}(1-x)^{2n-1}}{(1+x^{2})^{m+n}} \, dx $

definite and indefinite integral with hypergeometric function

Prove: $\int_0^2 \frac{dx}{\sqrt{1+x^3}}=\frac{\Gamma\left(\frac{1}{6}\right)\Gamma\left(\frac{1}{3}\right)}{6\Gamma\left(\frac{1}{2}\right)}$

Integral to Gamma function

Proving the monotonicity of an implicit function

Gamma and Beta function proof

Evaluating an integral using the beta, gamma and digamma functions

Reciprocal of Beta Function

What is relationship between beta and binomial distributions in Bayesian inference

Compute $\int_0^\infty\frac{x^{2r}}{(1+x^2)^m}\cdot \frac{\Gamma(m)}{\Gamma(1/2)\Gamma(m-1/2)}dx$ using the beta function

Value of integral $\int \frac{(1-x)^{n+1}}{x} dx$

Uniform rate of convergence of $\sum_{k=0}^{n} {2n+1\choose{k}}\left(a^{k+1}(1-a)^{(2n+1)-k}+a^{(2n+1)-k}(1-a)^{k+1}\right)$ to $\min(a,1-a)$

Asymptotic behavior of the CDF of a $\operatorname{Beta}(n,n)$ at $x<1/2$.

gamma functions as infinite series

Computing the value of $\int_0^\frac\pi2\frac{\sin^{2m-1}\theta\cos^{2n-1}\theta}{(a\sin^2\theta+b\cos^2\theta)^{m+n}}\,d\theta$

Trending Questions

Popular # Hahtags

Popular Questions