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## 26.3 Gamma

The gamma function, $$\Gamma(x)$$, is the generalization of the factorial function to continuous variables, defined so that for positive integers $$n$$, $\Gamma(n+1) = n!$ Generalizing to all positive numbers and non-integer negative numbers, $\Gamma(x) = \int_0^{\infty} u^{x - 1} \exp(-u) \,n du.$