List questions from beta-function

61

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Evaluating the integral $\int_{c/(1+c)}^{\infty}1/(v^c(v+1))dv$ ("generalized incomplete beta function")

Published on 05 Apr 2023 - 9:37

80

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Integrals involving Gamma Functions

Published on 20 Apr 2023 - 11:27

106

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Generate two uniform random variables, then take the interval between them

Published on 29 Apr 2023 - 5:10

61

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Why do the Beta and Binomial densities look exactly the same?

Published on 06 May 2023 - 5:30

44

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Integrate without using the property that the function is odd

Published on 23 Feb 2026 - 13:23

70

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Generalisation of a definite integral $I(a)$ with value independent of its parameter $a$.

Published on 16 May 2023 - 2:29

162

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Evaluating $\displaystyle\int_{0}^{\infty} \frac{{x}^{2/3}-{x}^{1/4}}{(1+{x}^{2})\ln(x)} dx$ using the gamma and beta functions

Published on 16 May 2023 - 13:13

83

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On a tricky integral and Euler's reflection formula

Published on 21 May 2023 - 20:00

83

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Evaluate: $\int_{0}^{\infty} x^{a} (1+x)^{b} dx$

Published on 02 Jun 2023 - 3:40

117

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Inverse of a gamma function

Published on 05 Jun 2023 - 11:09

69

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Compute the integral $\int_0^\infty t^{3/\xi-1} e^{-t} \Gamma(\frac{2}{\xi},t) \ dt$

Published on 08 Jun 2023 - 0:23

56

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Beta or Incomplete Beta Integral.

Published on 09 Jun 2023 - 7:45

57

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On bodies of revolution for $y =(1-x^q)^p$

Published on 26 Mar 2026 - 8:23

139

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A pattern among the polynomial integrals $\int_\alpha^\beta(x-\alpha)^j (x-\beta)^k\,dx$

Published on 28 Jun 2023 - 19:54

135

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Proving that $I=\int_0^\infty \frac{n x^{n-1}}{(1+x)^{n+1}}dx<+\infty$

Published on 30 Jun 2023 - 20:08

List Question

Evaluating the integral $\int_{c/(1+c)}^{\infty}1/(v^c(v+1))dv$ ("generalized incomplete beta function")

Integrals involving Gamma Functions

Generate two uniform random variables, then take the interval between them

Why do the Beta and Binomial densities look exactly the same?

Integrate without using the property that the function is odd

Generalisation of a definite integral $I(a)$ with value independent of its parameter $a$.

Evaluating $\displaystyle\int_{0}^{\infty} \frac{{x}^{2/3}-{x}^{1/4}}{(1+{x}^{2})\ln(x)} dx$ using the gamma and beta functions

On a tricky integral and Euler's reflection formula

Evaluate: $\int_{0}^{\infty} x^{a} (1+x)^{b} dx$

Inverse of a gamma function

Compute the integral $\int_0^\infty t^{3/\xi-1} e^{-t} \Gamma(\frac{2}{\xi},t) \ dt$

Beta or Incomplete Beta Integral.

On bodies of revolution for $y =(1-x^q)^p$

A pattern among the polynomial integrals $\int_\alpha^\beta(x-\alpha)^j (x-\beta)^k\,dx$

Proving that $I=\int_0^\infty \frac{n x^{n-1}}{(1+x)^{n+1}}dx<+\infty$

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