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Beta-doc.m2
doc /// Key Beta (Beta,CC,CC) (Beta,CC,RR) (Beta,RR,CC) (Beta,RR,RR) (Beta,RR,RRi) (Beta,RRi,RR) (Beta,RRi,RRi) Headline Beta function Usage Beta(x, y) Inputs x:RR y:RR Outputs :RR -- the beta function of @TT "x"@ and @TT "y"@ Description Text This is the @wikipedia "beta function"@ \(B(x,y) = \int_0^1 t^{x - 1}(1 - t)^{y - 1}\,dt\). Example Beta(3, 4) SeeAlso regularizedBeta inverseRegularizedBeta /// doc /// Key regularizedBeta (regularizedBeta,CC,CC,CC) (regularizedBeta,CC,CC,RR) (regularizedBeta,CC,RR,CC) (regularizedBeta,CC,RR,RR) (regularizedBeta,RR,CC,CC) (regularizedBeta,RR,CC,RR) (regularizedBeta,RR,RR,CC) (regularizedBeta,RR,RR,RR) (regularizedBeta,RR,RR,RRi) (regularizedBeta,RR,RRi,RR) (regularizedBeta,RR,RRi,RRi) (regularizedBeta,RRi,RR,RR) (regularizedBeta,RRi,RR,RRi) (regularizedBeta,RRi,RRi,RR) (regularizedBeta,RRi,RRi,RRi) Headline regularized beta function Usage regularizedBeta(x, a, b) Inputs x:RR a:RR b:RR Outputs :RR Description Text This is the regularized (incomplete) @wikipedia "beta function"@ \(I_x(a, b) = \frac{1}{B(a, b)}\int_0^x t^{a - 1} (1 - t)^{b - 1}\,dt\). Example regularizedBeta(1/2, 3, 4) 1/Beta(3,4) * integrate(t -> t^2 * (1 - t)^3, 0, 1/2) SeeAlso Beta inverseRegularizedBeta /// doc /// Key inverseRegularizedBeta (inverseRegularizedBeta,RR,RR,RR) Headline inverse of the regularized beta function Usage inverseRegularizedBeta(y, a, b) Inputs y:RR a:RR b:RR Outputs :RR Description Text This is the inverse of @TO regularizedBeta@ with respect to the first argument. Example regularizedBeta(1/2, 3, 4) inverseRegularizedBeta(oo, 3, 4) SeeAlso Beta regularizedBeta ///
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