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Re: What is the limit of x Gamma[n,x] for x->Infinity?

• To: mathgroup at smc.vnet.net
• Subject: [mg43965] Re: What is the limit of x Gamma[n,x] for x->Infinity?
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Thu, 16 Oct 2003 04:15:59 -0400 (EDT)
• Organization: Universitaet Leipzig
• References: <bmj2qp$prv$1@smc.vnet.net>
• Reply-to: kuska at informatik.uni-leipzig.de
• Sender: owner-wri-mathgroup at wolfram.com

Hi,

my Abramowitz/Stegun say

Gamma[a,x]= x^(a-1)*Exp[-x]*(1+(a-1)/x+ (a-1)*(a-2)/x^2+ ..)

and x Gamma[a,x] should be asymtotic run as

 x^a *Exp[-x]

an the limit is (beside strage a's) zero ..

Regards
  Jens

Xavier wrote:
> 
> If Gamma[n,x] is the incomplete Gamma function, what is the limit of
> that function times x when x tends to infinity?
> 
> At first blush this limit is indefinite since Gamma[n,x] ->0 when
> x->Infinity.
> 
> Any help is welcome!!!
> Thanks
> Xavier