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MathGroup Archive 2006

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Re: simplifying a summation / integral

  • To: mathgroup at smc.vnet.net
  • Subject: [mg64783] Re: simplifying a summation / integral
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Thu, 2 Mar 2006 19:28:00 -0500 (EST)
  • Organization: The Open University, Milton Keynes, UK
  • References: <du6nqk$5ob$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Patrik wrote:
> I need a simple closed form expression for:
> 
> Sum [(qCr)*(x^r)/r]
> where qCr is q choose r, i.e., (q!/(r!(q-r)!)
> and r is summed from 1 to q
> 
> Any thoughts?
Hi Patrik,

Do you mean something like that?

In[1]:=
Sum[Binomial[q, r]*(x^r/r), {r, 1, q}]

Out[1]=
q*x*HypergeometricPFQ[{1, 1, 1 - q}, {2, 2}, -x]

Best regards,
/J.M.


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