Gamma Distribution?

Question

So the formula for solving Gamma(k) is G(k) = (k - 1)*G(k-1) - and the special cases are G(.5) and G(1) = sqrt(pi) - but how do you solve G(1.25) or something like that? That would become .25*G(.25), meaning you'd have to solve for G(.25)... how do you solve for that?

Answer 1

Those values you can find in a chart.

Also you could use a graphing calculator or some other solver to get the integral you want.
gamma(1.25) = Int(y^.25*e^ y)

Answer 2

You're talking about the gamma function, not the gamma distribution (which is a common probability distribution we study in statistics; I believe the Chi-Squared distribution is a special type of gamma distribution). The gamma function is actually given as an integral (I can't remember it at the moment....it involves an e^{-x}) and G(k)=(k-1)G(k-1) really only holds for inetgers I think, so G(k)=(k-1)! (so G(1)=1, not sqrt{pi}; I believe G(0.5)=sqrt{pi}).

Truth be told the gamma function isn't an easy thing to understand so if it's not clear right now then I guess maybe wait until you take a stats or number theory class and learn about it then. It's actually quite important (it comes up in the formulation of the generalized Riemann Zeta Function).

Answer 3

Try here.

http://www.nr.com/forum/showthread.php?p=1562