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MathGroup Archive 2003

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

  • To: mathgroup at smc.vnet.net
  • Subject: [mg43968] Re: [mg43956] What is the limit of x Gamma[n,x] for x->Infinity?
  • From: Vladimir Bondarenko <vvb at mail.strace.net>
  • Date: Thu, 16 Oct 2003 04:16:01 -0400 (EDT)
  • References: <200310150859.EAA26398@smc.vnet.net>
  • Reply-to: Vladimir Bondarenko <vvb at mail.strace.net>
  • Sender: owner-wri-mathgroup at wolfram.com

xavier.brusset at free.fr (Xavier) write on Wednesday, October 15, 2003, 11:59:34 AM:

X> If Gamma[n,x] is the incomplete Gamma function, what is the limit of
X> that function times x when x tends to infinity?
X> At first blush this limit is indefinite since Gamma[n,x] ->0 when
x->>Infinity.

The correct answer is zero.

   In[1] := Normal[Series[Gamma[n, x] x, {x, Infinity, 1}]]
   Out[1] = (x^(-1 + n)*(-1 + n + x))/E^x

Now the exponent devours quickly the polynomial of any degree.

   In[2] := Limit[Gamma[n, x] x, x -> Infinity]
   Out[2] = 0


Best regards,

Vladimir Bondarenko

CEO, Mathematical Director
Cyber Tester, LLC
www.cybertester.com


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