List questions from beta-function

Published on 23 Mar 2026 - 2:40

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Find the value of $A+B+C$ in the following question?

Published on 19 Mar 2026 - 20:45

138

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How to prove that $\int_0^1 \frac{x^{1-p}(1-x)^pdx}{x^2+1}=\frac{\pi}{\sin px}(2^{\frac{p}{2}}\cos {\frac{p\pi}{4}}-1)$

Published on 23 Mar 2026 - 7:18

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Question related to beta and gamma function

Published on 22 Mar 2026 - 20:59

120

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Integrating $\int_{0}^{1} x^a (c-x)^b dx $

Published on 22 Mar 2026 - 17:52

62

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Correct interpretation + implementation of Beta Binomial sampling function?

Published on 23 Mar 2026 - 2:40

114

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Integrating $\int_{0}^{1} x^a (1-x)^b (1-2x)^c \, \mathrm dx $

Published on 22 Mar 2026 - 15:03

347

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Beta function solution for $\int_0^2(16-x^2)^{-3/2}\,dx$

Published on 22 Mar 2026 - 23:26

365

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Is it possible to evaluate this integral using beta and gamma functions?

Published on 22 Mar 2026 - 15:18

85

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To show that $\exp(\psi(2n+1))\int_0^1x^n(1-x)^n dx$ is a positive integer, where $\psi(x)$ is the Chebyshev function

Published on 23 Mar 2026 - 1:16

2.4k

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Laplace transform to prove relationship between the Gamma and Beta functions

Published on 22 Mar 2026 - 22:56

252

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If I ask $2N$ people a yes or no question, what's the probability $N$ say yes?

Published on 23 Mar 2026 - 8:56

2.8k

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Writing the Beta Function in terms of the Gamma Function

Published on 23 Mar 2026 - 14:21

269

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Show that $ \sum_{k=0}^{j} \binom{2j+1}{k+j+1} \ \frac{(-1)^k}{2k+1}=2^{2j-1}\ B(j+1,1/2)$.

Published on 23 Mar 2026 - 9:23

70

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How can I get the result?

Published on 22 Mar 2026 - 17:03

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Calculating integral using pdf's $\int_0^1x^r(1-x)^{n-r}dx$

Find the value of $A+B+C$ in the following question?

How to prove that $\int_0^1 \frac{x^{1-p}(1-x)^pdx}{x^2+1}=\frac{\pi}{\sin px}(2^{\frac{p}{2}}\cos {\frac{p\pi}{4}}-1)$

Question related to beta and gamma function

Integrating $\int_{0}^{1} x^a (c-x)^b dx $

Correct interpretation + implementation of Beta Binomial sampling function?

Integrating $\int_{0}^{1} x^a (1-x)^b (1-2x)^c \, \mathrm dx $

Beta function solution for $\int_0^2(16-x^2)^{-3/2}\,dx$

Is it possible to evaluate this integral using beta and gamma functions?

To show that $\exp(\psi(2n+1))\int_0^1x^n(1-x)^n dx$ is a positive integer, where $\psi(x)$ is the Chebyshev function

Laplace transform to prove relationship between the Gamma and Beta functions

If I ask $2N$ people a yes or no question, what's the probability $N$ say yes?

Writing the Beta Function in terms of the Gamma Function

Show that $ \sum_{k=0}^{j} \binom{2j+1}{k+j+1} \ \frac{(-1)^k}{2k+1}=2^{2j-1}\ B(j+1,1/2)$.

How can I get the result?

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