Re: Wrong Limit

*To*: mathgroup at smc.vnet.net*Subject*: [mg47790] Re: [mg47775] Wrong Limit*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Tue, 27 Apr 2004 04:46:33 -0400 (EDT)*References*: <200404260641.CAA06357@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

First of all, Mathematica 5.0 gives: Sum[1/k^p, {k, 1, Infinity}] Zeta[p] which is correct so there is no real need to take any limits. Still, your observation seems to reveal a bug in Mathematica 5.0. which may be related to one that was already discussed here recently. First, look at this: Sum[1/k^3,{k,1,m}] HarmonicNumber[m, 3] + PolyGamma[2, 1]/2 + Zeta[3] This looks strange, but in fact is correct since: FullSimplify[PolyGamma[2,1]/2+Zeta[3]] 0 Now FullSimplify[Sum[1/k^3,{k,1,m}]] PolyGamma[2, 1 + m]/2 + Zeta[3] This is still correct: PolyGamma[2,1+m]/2==HarmonicNumber[m,3]+PolyGamma[2,1]/2//FullSimplify True However, it tells us that Limit[PolyGamma[2, 1 + m]/2,m->Infinity] ought to be zero, while Mathematica gives: Limit[PolyGamma[2,1+m]/2,m->Infinity] Infinity Andrzej Kozlowski Chiba, Japan http://www.mimuw.edu.pl/~akoz/ On 26 Apr 2004, at 15:41, Ray wrote: > In Mathematica 4.2, if s[n_]:= Sum[1/k^p,{k,1,n}], then the output for > Limit[s[n],n->Infinity] was Limit[HarmonicNumber[n,p],n->Infinity]. > Under 5.0.1, the answer to Limit[s[n],n->Infinity] is given incorrectly > as Infinity for odd p and the actual numerical value for even p. Anyone > know why Mathematica now gives an incorrect result here for odd p. > Thanks. > > >

**References**:**Wrong Limit***From:*Ray <rayfg@optonline.net>