From owner-cse191-sp08-list@LISTSERV.BUFFALO.EDU Fri Mar 21 12:58:08 2008 Date: Fri, 21 Mar 2008 12:53:50 -0400 From: "William J. Rapaport" Subject: 191: Non-Recursive Factorial Function To: CSE191-SP08-LIST@LISTSERV.BUFFALO.EDU > Date: Fri, 21 Mar 2008 10:06:08 -0400 > From: Matt Heavner > To: "William J. Rapaport" > Subject: CSE191 - Function equal to factorial function > > Professor Rapaport, > > You mentioned in class that you hadn't found a function that is equal to > the factorial function, if I remember correctly. I'm in MTH411, > Probability Theory, and we just covered a function that, while not > "easy", is actual equal to the factorial function - the gamma function. > > The wikipedia entry shows this - http://en.wikipedia.org/wiki/Gamma_function > > Maybe you've seen this before? > > - Matt Heavner > > Date: Fri, 21 Mar 2008 10:59:50 -0400 (EDT) > From: "William J. Rapaport" > To: mheavner@buffalo.edu, rapaport@cse.Buffalo.EDU > Subject: Re: CSE191 - Function equal to factorial function > > Thanks! I had seen it, but hadn't realized the exact connection; > thanks for pointing this out. Another nice example of a recursive > definition that's a lot friendlier than the non-recursive version! For those of you who might not want to read the entire Wikipedia article, GAMMA is a function over complex numbers. Briefly, GAMMA(z) = INTEGRAL from 0 to infty of (t^(z-1)e^-t dt (You don't have to understand that; you just have to realize that it's not as nice as the recursive definition of factorial. It turns out that GAMMA(n) = (n-1)! (It also turns out that (GAMMA(1/2))^2 = pi, which I think is pretty amazing, too.)