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MathGroup Archive 2005

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Re: Problem with RSolve

  • To: mathgroup at smc.vnet.net
  • Subject: [mg62678] Re: [mg62670] Problem with RSolve
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Wed, 30 Nov 2005 22:08:41 -0500 (EST)
  • Reply-to: hanlonr at cox.net
  • Sender: owner-wri-mathgroup at wolfram.com

$Version

5.2 for Mac OS X (June 20, 2005)

Clear[a,c,n];

a[0]=0;
a[n_Integer?Positive]:=
    a[n]=a[n-1]+(n^2) Log[n];

Table[a[n],{n,0,5}]//Simplify

{0, 0, Log[16], Log[314928], 9*Log[3] + 16*Log[4] + Log[16], 
  9*Log[3] + 16*Log[4] + 25*Log[5] + Log[16]}

RSolve gives a wrong result

soln=c[n]/.
    (RSolve[{c[n]==c[n-1]+(n^2) Log[n],
              c[0]==0},c[n],n]//
          Flatten//FullSimplify)

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

Table[soln,{n,0,5}]//FullSimplify

{0, -(35/9), -(239/18) + Log[16], -(61/2) + Log[314928], 
  -(521/9) + 36*Log[2] + 9*Log[3], -(880/9) + 36*Log[2] + 
   9*Log[3] + 25*Log[5]}


Bob Hanlon

> 
> From: Jean Guillaume Pyraksos <wissme at hotmail.com>
To: mathgroup at smc.vnet.net
> Date: 2005/11/30 Wed AM 05:40:43 EST
> Subject: [mg62678] [mg62670] Problem with RSolve
> 
> 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
> 
> 


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