TITLE: Who invented the gamma function?
QUESTION [20 upvotes]: Who was the first person who solved the problem of extending the factorial to non-integer arguments? 
Detlef Gronau writes [1]: "As a matter of fact, it was Daniel Bernoulli who gave in 1729 the first representation of an interpolating function of the factorials in form of an infinite product, later known as gamma function."
On the other hand many other places say it was Leonhard Euler. Will the real inventor please stand up? 
[1] "Why is the gamma function so as it is?" by Detlef Gronau, Teaching Mathematics and Computer Science, 1/1 (2003), 43-53.

REPLY [8 votes]: In his first letter to Goldbach (already linked to in Jonas' answer) Euler writes that he communicated his interpolation of the sequence of factorials (or Wallis's hypergeometric series, as it was called back then) to Daniel Bernoulli:
"I communicated this to Mr. Bernoulli, who by his own method arrived at nearly the same final expression" (this is the sentence starting with "communicavi haec . . . " on p. 4).