Definition:Gamma Function/Euler Form/Historical Note

Historical Note on Euler Form of Gamma Function

Leonhard Paul Euler was the first to find this extension of the factorial to the real numbers.

He actually specified it in the form:

$\ds n! = \lim_{m \mathop \to \infty} \frac {m^n m!} {\paren{n + 1} \paren{n + 2} \cdots \paren{n + m}}$

He wrote to Christian Goldbach about it in a letter dated $13$th October $1729$.

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: $(13)$