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This question already has an answer here:

Is there a law or anyway to know the factorial of a fractional number, because as I see the law of factorization n! = n x (n-1) x (n-2) x ... x 3 x 2 x 1 isn't saying that the number should be an integer. If it does require an integer then shouldn't the law be [n]! = [n] x ([n]-1) x ([n]-2) x ...?

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marked as duplicate by user147263, Leucippus, Chris Godsil, colormegone, Milo Brandt Apr 8 '16 at 0:48

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check out the Gamma function, an extension of the factorial function to the real (and complex) numbers

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