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.

```

• Prev by Date: Re: Re: Re: function of a function
• Next by Date: Re: Problem with RSolve
• Previous by thread: Re: Re: Re: function of a function
• Next by thread: Re: Problem with RSolve