Incomplete Gamma function
- To: mathgroup at smc.vnet.net
- Subject: [mg67619] Incomplete Gamma function
- From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
- Date: Sun, 2 Jul 2006 06:27:59 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Here is a question I have come across concerning special functions, which unfortunately, is an area of mathematics I know next to nothing about. However, as there are many experts in this field who read this list I hope someone will find this an interesting (or trivial?) question. Consider the following sequence: Table[FunctionExpand[Exp[n-1]*Gamma[n,n-1]],{n,2,14}] {2,10,78,824,10970,176112,3309110,71219584,1727242866,46602156800, 1384438376222,44902138752000,1578690429731402} As you see, we get only integers. What happens if n is larger than 14? Mathematica seems not to be able to answer this: FunctionExpand[Exp[n - 1]* Gamma[n, n - 1]] /. n -> 15 E^14*Gamma[15, 14] Numerical methods also do not seem to be able to determine if this is an integer or not. I have looked at Abramowitz & Stegun but I can't see anything that obviously helps to resolve the issue. Can anyone help? Andrzej Kozlowski Tokyo, Japan