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.