MathGroup Archive 2006

[Date Index] [Thread Index] [Author Index]

Search the Archive

RE: Incomplete Gamma function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg67764] RE: [mg67619] Incomplete Gamma function
  • From: "Erickson Paul-CPTP18" <Paul.Erickson at Motorola.com>
  • Date: Thu, 6 Jul 2006 06:54:39 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Try
http://www.research.att.com/~njas/sequences/?q=2%2C+10%2C+78&language=en
glish&go=Search

Based on the matching of the first 15 terms, the engineer in me say this
is the same thing. The mathematician, well ??? It's a good start. The
site lists a few more terms, and perhaps more important give equations,
etc.

In general a very useful resource.

Paul

 

-----Original Message-----
From: Andrzej Kozlowski [mailto:akoz at mimuw.edu.pl] 
To: mathgroup at smc.vnet.net
Subject: [mg67764] [mg67619] Incomplete Gamma function

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


  • Prev by Date: Re: Plot Question
  • Next by Date: Re: random inside module
  • Previous by thread: Re: Incomplete Gamma function
  • Next by thread: finite differencing of a PDE system