       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/

```

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