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Is it possible to obtain the Stirling approximation for the factorial by using the gamma function ? $$\Gamma(z) = \lim_{n \to +\infty} \frac{n! n^{z}}{z(z+1) \dots (z+n)}$$

Any hint ?

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Using the limit formula: http://www.sms.edu.pk/journals/jprm/jprmvol8/01.pdf.

Using the integral formula: http://www.math.unl.edu/~sdunbar1/ProbabilityTheory/Lessons/StirlingsFormula/GammaFunction/gammafunction.pdf.

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