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MathGroup Archive 2005

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Re: Problem with RSolve

  • To: mathgroup at smc.vnet.net
  • Subject: [mg62685] Re: Problem with RSolve
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Wed, 30 Nov 2005 22:08:52 -0500 (EST)
  • Organization: The Open University, Milton Keynes, UK
  • References: <dmk02k$781$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Jean Guillaume Pyraksos wrote:
> I can't get this one solved, can you help ?
> 
> RSolve[{c[n] == c[n - 1] + (n^2) Log[n], c[0] == 0}, c[n], n]
> 
> I am interested in the principal part of c[n], which should be 1/2 n^2 
> Log[n]^2 ?...
> 
> Thanks, using Mathematica 4.1.0.0
> 
>    JG
> 
Hi Jean Guillaume,

Here is what I get, after simplification, with Mathematica 5.2 for Windows:

In[1]:=
FullSimplify[c[n] /. RSolve[
     {c[n] == c[n - 1] + n^2*Log[n], c[0] == 0}, c[n],
     n]]

Out[1]=
{(-(1/36))*n*(69 + n*(57 + 14*n)) +
    (1 + n)^2*Log[Gamma[1 + n]] -
    (1 + n)^2*Log[Gamma[2 + n]] + Zeta[3]/(4*Pi^2) +
    Derivative[1, 0][Zeta][-2, 2 + n]}

In[3]:=
$Version

Out[3]=
"5.2 for Microsoft Windows (June 20, 2005)"

Hope this helps,
/J.M.


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