Factorial of Half/Historical Note

Historical Note on Factorial of Half

The factorial of $\dfrac 1 2$ was deduced by James Stirling during the course of his attempt to extend the factorial to the real numbers.

However he was not able to prove that such an extension defined $n!$ for a general non-integer $n$.

Sources

• 1997: Donald E. Knuth: The Art of Computer Programming: Volume 1: Fundamental Algorithms (3rd ed.) ... (previous) ... (next): $\S 1.2.5$: Permutations and Factorials