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Use Beta Function Identity to Prove the Equality

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#beta-function
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Definite integration of Bernoulli likelihood

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#integration #definite-integrals #binomial-distribution #beta-function
489
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How to calculate $\int_0^1\frac{\ln^2x\ln^2(1-x^2)}{1-x^2}\ dx$?

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#real-analysis #calculus #integration #harmonic-numbers #beta-function
497
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Proving that $\int_0^\infty\Big(\sqrt[n]{1+x^n}-x\Big)dx~=~\frac12\cdot{-1/n\choose+1/n}^{-1}$

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#calculus #integration #definite-integrals #closed-form #beta-function
648
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Approximating the Digamma fucntion near 1

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#numerical-methods #systems-of-equations #functional-equations #gamma-function #beta-function
836
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Mean Absolute Deviation for a Stable Distribution as a Function of the Tail Exponent

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#probability-theory #probability-distributions #numerical-methods #characteristic-functions #beta-function
193
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Log integrals II

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#integration #definite-integrals #logarithms #closed-form #beta-function
394
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Definite integral similar to beta function but with exponential negative square root

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#integration #definite-integrals #beta-function
763
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Why does β=α give a symmetric standard beta pdf?

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#statistics #beta-function
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Harmonic number identity

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#calculus #sequences-and-series #binomial-coefficients #harmonic-numbers #beta-function
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$E[X^2]$ of the Beta Distribution

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#statistics #probability-distributions #beta-function
90
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Calculate $\int_{0}^t (0.3(1+x)^3+0.7)^{-1/2}\,dx$

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#integration #hypergeometric-function #elliptic-integrals #beta-function
55
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Beta density function

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#probability-distributions #beta-function
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Product of two Beta distributed random variables

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#probability-distributions #beta-function
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Integral over a simplex

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#integration #simplex #beta-function

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