General Factorial
Problem
The Gamma function is defined as, Γ($x$) | = |
| $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.
Problem ID: 251 (02 Dec 2005) Difficulty: 4 Star