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General Factorial

Problem

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


0
$t$$x$minus1 $e$minus$t$ $dt$.

Given that Γ($x$) is continuous for $x$ greater than 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

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