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My TI-83 calculator doesnt allow me to do this, but using Windows calculator, I can compute the factorial of say 5.8. What does this mean and how does it work?

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As I recall, these calculators can compute factorials of half-integers. But yes, you need $\Gamma(z)$ in general. –  J. M. Nov 28 '10 at 1:29

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up vote 12 down vote accepted

Perhaps you're looking for the Gamma function. It restricts to the usual factorial on natural numbers.

Wikipedia's article on Gamma function

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Wow thats crazy. Thanks –  maq Nov 27 '10 at 20:15

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