## General Factorial

#### Problem

The Gamma function is defined as, Γ(x) | = |
| t^{x1} 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