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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>