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Mathematically prove that a Beta prior distribution is conjugate to a Geometric likelihood function

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#bayesian #maximum-likelihood #beta-function
130
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How do I evaluate $\int_{0}^{t} x^{\alpha+k-1}(t-x)^{\beta+k-1} dx$?

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#real-analysis #integration #gamma-function #beta-function
586
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Prove an transformation formula for Gauss hypergeometric function $_2F_1(a,b;c;z)$

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#power-series #special-functions #gamma-function #hypergeometric-function #beta-function
166
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Solution of $\int_x^1y^{a-1}\left(1-y\right)^{b-1}dy = \left(2\frac{x+1}{x+2}\right)x^{a}\left(1-x\right)^{b-1}$

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#definite-integrals #estimation #beta-function
616
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What are the poles and zeros of the Euler Beta function?

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#special-functions #beta-function
46
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Integral $\int_{a}^s\int_{a}^u\frac{1}{\sqrt{s-u}\sqrt{u-v}\sqrt{v-a}}dvdu$

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#real-analysis #integration #beta-function
110
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Calculate $ \int_{0}^{\pi} \frac{dx}{\sqrt{3-\cos(x)}} $

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#calculus #integration #gamma-function #beta-function
54
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conditonal distribution question

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#probability #probability-distributions #conditional-probability #beta-function
100
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Beta function in Philip J. Davis׳ Essay

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#calculus #special-functions #beta-function
122
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Peculiar (convergent?) definite integral

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#calculus #definite-integrals #gamma-function #beta-function
1.4k
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Is a Beta distribution a continuous version of the Binomial Theorem?

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#probability-distributions #binomial-distribution #beta-function
455
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Sum involving incomplete beta functions

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#integration #asymptotics #special-functions #hypergeometric-function #beta-function
49
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minimizing a double integral including beta function

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#optimization #beta-function
1.4k
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Asymptotic expansion of incomplete beta function

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#real-analysis #asymptotics #taylor-expansion #special-functions #beta-function
910
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Beta function and gamma function

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#integration #factorial #gamma-function #beta-function

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