       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)
• Sender: owner-wri-mathgroup at wolfram.com

```\$Version

5.2 for Mac OS X (June 20, 2005)

Clear[a,c,n];

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

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

{0, 0, Log, Log, 9*Log + 16*Log + Log,
9*Log + 16*Log + 25*Log + Log}

RSolve gives a wrong result

soln=c[n]/.
(RSolve[{c[n]==c[n-1]+(n^2) Log[n],
c==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/(4*Pi^2)

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

{0, -(35/9), -(239/18) + Log, -(61/2) + Log,
-(521/9) + 36*Log + 9*Log, -(880/9) + 36*Log +
9*Log + 25*Log}

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}, 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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