mathschallenge.net

Problem

The Gamma function is defined as, Γ($x$)

=

0

$t$$x$1 $e$$t$ $dt$.

Given that Γ($x$) is continuous for $x$ 0 prove that Γ($x$ + 1) = $x$! for all positive integer values, and consequently is a candidate for extending the factorial function to non-integer positive values.