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