Symbolic Computation
The beta function is a special function denoted as $$B(x, y)$$, defined by the integral $$B(x, y) = \int_0^1 t^{x-1} (1 - t)^{y-1} dt$$ for positive real numbers $$x$$ and $$y$$. This function has strong connections to various areas of mathematics, particularly in evaluating integrals and relating to the gamma function, which is another significant special function used in probability, statistics, and combinatorics.
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