Re: Troubles with HarmonicNumber, empty sums, and Zeta

*To*: mathgroup at smc.vnet.net*Subject*: [mg85554] Re: [mg85519] Troubles with HarmonicNumber, empty sums, and Zeta*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Wed, 13 Feb 2008 06:58:52 -0500 (EST)*References*: <200802130915.EAA21588@smc.vnet.net>

On 13 Feb 2008, at 10:15, David W.Cantrell wrote: > > > In[27]:= N[Zeta[-1/2] - Zeta[-1/2, -2]] > Out[27]= -2.41421 > > [BTW, is there some reasonably direct way to simplify > Zeta[-1/2] - Zeta[-1/2, -2] to -1 - Sqrt[2] using Mathematica?] > > David W. Cantrell > It depends on the meaning of "direct". But there certainly is a "short" way: RootApproximant[Zeta[-2^(-1)] - Zeta[-2^(-1), -2]] -1 - Sqrt[2] Andrzej Kozlowski

**References**:**Troubles with HarmonicNumber, empty sums, and Zeta***From:*"David W.Cantrell" <DWCantrell@sigmaxi.net>