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{\Gamma(t)} = {\int_{0}^{+\infty} x^{t-1} e^{-x} dx} = {\frac{1}{t} \prod_{n=1}^\infty \frac{\left(1+\frac{1}{n}\right)^t}{1+\frac{t}{n}} } \sim {\sqrt{\frac{2\pi}{t}} \left(\frac{t}{e}\right)^t}