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Dirichlet’s Theorem and Liouville’s Extension of Dirichlet’s Theorem

Thursday, February 24th, 2011 17:30 / Leave a Comment

Topic

Beta & Gamma functions

Statement

$\int \, \int \, \int_{V} \, x^{l-1} y^{m-1} z^{n-1} dx \, dy \,dz = \frac { \Gamma {(l)} \Gamma {(m)} \Gamma {(n)} }{ \Gamma{(l+m+n+1)} }$
where V is the region given by $x \ge 0, y \ge 0, z \ge 0, \, x+y+z \le 1$ .

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MY DIGITAL NOTEBOOK

Tag Archives: gamma

Dirichlet’s Theorem and Liouville’s Extension of Dirichlet’s Theorem

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