Double FactorialDate: 02/22/2002 at 03:06:42 From: Linda Mitchell Subject: Factorial !! Hi Dr Math. Please can you tell me what TWO ! marks mean in factorial questions? For example (1/.2)!! is an expression I have seen, but while I understand that the first ! would mean 5*4*3*2*1, I have no idea what the second ! does to it. Thank you, Linda M. Date: 02/22/2002 at 04:03:35 From: Doctor Pete Subject: Re: Factorial !! Hi Linda, The notation of two factorials, e.g., x!! is a single symbol, called the double factorial. It is the product of every other positive integer less than or equal to x, so for instance, 9!! = 9*7*5*3*1, and 12!! = 12*10*8*6*4*2. This is not to be confused with a repeated factorial, which would be written (x!)!, where we would have for the case x = 5, (5!)! = 120!, a much larger number than 5!! = 15. It is not too difficult to show that if n is even, then n!! = (2^(n/2))(n/2)!, and if n is odd, then n!! = n!/(n-1)!! = n!/(2^((n-1)/2)((n-1)/2)!); thus revealing a relation between the double and single factorial functions. - Doctor Pete, The Math Forum http://mathforum.org/dr.math/ |
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