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Re: Problem with RSolve

• To: mathgroup at smc.vnet.net
• Subject: [mg62689] Re: Problem with RSolve
• From: "Scout" <Scout at nodomain.com>
• Date: Wed, 30 Nov 2005 22:09:05 -0500 (EST)
• References: <dmk02k$781$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

"Jean Guillaume Pyraksos" <wissme at hotmail.com> ha scritto nel messaggio 
news:dmk02k$781$1 at smc.vnet.net...
>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,
I've tried the recurrent equation on my system.
I get these results:

"4.0 for Microsoft Windows (April 21, 1999)":
{}
no solutions  with Indeterminate expressions and PolyLog syntax error :-(

Instead,
"5.2 for Microsoft Windows (June 20, 2005)":

In[]:= RSolve[{c[n] == c[n - 1] + (n^2) Log[n], c[0] == 0}, c[n], n]
Out[]=
\!\(\*
  RowBox[{"{",
    RowBox[{"{",
      RowBox[{\(c[n]\), "\[Rule]",
        RowBox[{\(1\/36\), " ",
          RowBox[{"(",

            RowBox[{\(\(-69\)\ n\), "-", \(57\ n\^2\), "-", \(14\ n\^3\),
              "+", \(36\ Log[Gamma[1 + n]]\),
              "+", \(72\ n\ Log[Gamma[1 + n]]\),
              "+", \(36\ n\^2\ Log[Gamma[1 + n]]\),
              "-", \(36\ Log[Gamma[2 + n]]\),
              "-", \(72\ n\ Log[Gamma[2 + n]]\),
              "-", \(36\ n\^2\ Log[Gamma[2 + n]]\), "-",
              RowBox[{"36", " ",
                RowBox[{
                  SuperscriptBox["Zeta",
                    TagBox[\((1, 0)\),
                      Derivative],
                    MultilineFunction->None], "[", \(\(-2\), 2\), "]"}]}],
              "+",
              RowBox[{"36", " ",
                RowBox[{
                  SuperscriptBox["Zeta",
                    TagBox[\((1, 0)\),
                      Derivative],
                    MultilineFunction->None], "[", \(\(-2\), 2 + n\),
                  "]"}]}]}], ")"}]}]}], "}"}], "}"}]\)


Regards,
    ~Scout~