During my study I find a form for gamma function it was $\Gamma (x) = \lim_{n\to\infty} \frac{n! n^{x-1}}{x(x-1)(x-2)........(x+n-1)}$ And then by simplify this limit I get $$\lim_{n\to\infty} \frac{n^{x-1}}{{x+n-1\choose n}}$$ then I use Stirling's approximation and evaluate the limit to $\ (x-1)! * e^{x-1} * (\frac{n}{n+x-1})^{x+n-1{\over2}}$$ What next I should do to get Gamma function from this limit ?
2026-04-04 18:49:38.1775328578
Gamma function still hard for me
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