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

**References**:**What is the limit of x Gamma[n,x] for x->Infinity?***From:*xavier.brusset@free.fr (Xavier)