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General Factorial

Problem

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


0
txminus1 eminust 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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