My Math Forum (-0.5)!^2 = π? why?

 Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion

 April 10th, 2015, 05:53 AM #1 Newbie   Joined: Apr 2015 From: Finland Posts: 1 Thanks: 0 (-0.5)!^2 = π? why? Why does ((-0.5)!)^2 equal pi? To me it really doesnt make sense since of what i know of you cant even factorial negative numbers right??
 April 10th, 2015, 06:15 AM #2 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 The "standard" definition of factorial is only for non-negative integers but it can be extended. It can, for example, be proven that the gamma function $\displaystyle \Gamma(n)= \int_0^\infty t^{n-1} e^{-t}dt= (n-1)!$ for n any positive integer. Even that integral is not defined for n a negative integer but it can be calculated for half integer, positive or negative, by an "integration by parts". Here "(-0.5)!)" is to be interpreted $\displaystyle \Gamma(0.5)= \int_0^\infty t^{1/2}e^{-t}dt$.

 Tags 052, factorial, negative, pi number, question

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