Finding the Factorial of Non-Integers
Date: 01/06/2005 at 09:59:13 From: Raffaele Subject: Fractions and factorials Hi, I know that non-negative integers can be computed as factorials. For example, 5! = 5*4*3*2*1. I have no problem with this but I notice on my calculator that if I type in say 3.5! it would return a defined number. If you can find the factorial of non-negative REAL numbers then how do you calculate them and is it possible to think about them geometrically? Thanks in advance, Raffaele
Date: 01/06/2005 at 11:07:22 From: Doctor Vogler Subject: Re: Fractions and factorials Hi Raffaele, Thanks for writing to Dr Math. That's a good question. Technically, the factorial only has meaning for nonnegative integers (0, 1, 2, 3, etc.). But there is a smooth function which is defined for all positive real numbers (in fact, for all real and complex numbers except the negative integers) and equals the factorial for all positive integers. The function is called the Gamma Function and satisfies gamma(n + 1) = n! for all nonnegative integers n. So some computers and calculators will, when asked to compute x!, prefer to give gamma(x + 1) instead of saying "ERROR" (or "E"), since people don't like to get errors. For more information on the gamma function, search our archives for "gamma function" or look at the MathWorld site at Gamma Function http://mathworld.wolfram.com/GammaFunction.html If you have any questions about this or need more help, please write back and show me what you have been able to do, and I will try to offer further suggestions. - Doctor Vogler, The Math Forum http://mathforum.org/dr.math/
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