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I know that factorial is also represented by Gamma function and we have exact value of factorial of (1/2), can someone help me how to find numerically(approximate) the factorial of positive fractions like (1/3) and (1/4) etc. Is it like instead of upper bound of gamma function as infinite we take some large values and try to do numerical integration ?

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    $\begingroup$ You pretty much have to do it numerically. $\endgroup$ – J.G. Jun 5 at 5:29
  • $\begingroup$ en.wikipedia.org/wiki/Particular_values_of_the_gamma_function is worth a look. $\endgroup$ – Barry Cipra Jun 5 at 5:49
  • $\begingroup$ Depending on the kind of precision you are looking for, you can use Striling's formula $$ \Gamma(z) \approx \sqrt{\frac{2 \pi}{z}}\left(\frac{z}{e}\right)^z $$ $\endgroup$ – PierreCarre Jun 5 at 7:32

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