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.