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

*To*: mathgroup at smc.vnet.net*Subject*: [mg43987] Re: [mg43956] What is the limit of x Gamma[n,x] for x->Infinity?*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Thu, 16 Oct 2003 04:16:52 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

On Wednesday, October 15, 2003, at 05:59 PM, 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 > > > The answer is 0 which is exactly what Mathematica gives: Limit[x Gamma[n,x],x->Infinity] 0 This follows very easily fro the L'Hospital rule Limit[x Gamma[n, x], x -> Infinity] == Limit[ Gamma[n, x]/(1/x), x -> Infinity] == Limit[D[ Gamma[n, x], x]/D[1/x, x], x -> Infinity] and D[Gamma[n, x], x]/D[1/x, x] x^(1 + n)/E^x etc. Andrzej Kozlowski Yokohama, Japan http://www.mimuw.edu.pl/~akoz/ http://platon.c.u-tokyo.ac.jp/andrzej/