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help deriving Beta function as a ratio of Gamma functions

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#calculus #integration #gamma-function #beta-function
55
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Doubt in the proof of Gamma Function

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#calculus #definite-integrals #improper-integrals #gamma-function #beta-function
86
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Doubt in substitution for a Gamma Function

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#calculus #definite-integrals #improper-integrals #gamma-function #beta-function
100
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Distribution of N smallest uniformly distributed random variables

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#uniform-distribution #poisson-distribution #order-statistics #beta-function
175
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How do you generate 10 values from a beta distribution?

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#statistics #simulation #beta-function
72
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Integral $\int_{-\infty}^{\infty} \frac{1-x}{1-x^5}\, d x $

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#real-analysis #calculus #integration #special-functions #beta-function
124
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Showing that $\sum_{k=0}^{n}{m+k\choose m}^{-1}=\frac{m}{m-1}\left[1-{m+n\choose m-1}^{-1}\right],m>1.$

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#sequences-and-series #summation #binomial-coefficients #binomial-theorem #beta-function
61
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How to calculate this fractional integral?

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#integration #definite-integrals #beta-function #fractional-calculus
139
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Should I call this distribution a Beta distribution?

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#probability-distributions #special-functions #gamma-function #beta-function #gamma-distribution
543
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evaluate beta function

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#calculus #gamma-function #beta-function
106
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Beta-Binomial Pmf

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#probability #probability-distributions #beta-function
64
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See $\int_0^{\infty}\frac{x^2}{(1+x)^{n-1}}$ as a Beta distribution

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#real-analysis #calculus #integration #probability-distributions #beta-function
175
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Generalizing $\sum_{n=1}^\infty \frac{\Gamma(n)\Gamma(x)}{\Gamma(n+x)} = \frac1{x-1}$ to double sum

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#sequences-and-series #gamma-function #beta-function
102
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Elementary closed form of $\exp\left(b\int_0^x \frac{t^{a-1}}{1-t^b}dt\right);a,b\in\Bbb N$

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#closed-form #products #rational-functions #beta-function #elementary-functions
105
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Ramanujan 1920 paper ; question on some definite integrals

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#definite-integrals #fourier-transform #gamma-function #beta-function

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