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Odd result from Sum

• To: mathgroup at smc.vnet.net
• Subject: [mg49673] Odd result from Sum
• From: Richard Gass <gass at physics.uc.edu>
• Date: Tue, 27 Jul 2004 07:00:57 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

Here is an odd result from Sum.  I tried to do the infinite sum below 
in version 5. Notice the result contains  System`HypergeometricDump`k 
and System`HypergeometricDump`k^2. I get the same answer under both OS 
X and Windows EXP. Does anyone know what is going on?

In[293]:=
Sum[(-1)^n*((2*n + 1)/
     (z^2 + n*((n + 1)/2))),
   {n, 0, Infinity}]

Out[293]=
-(((-1 + Sqrt[1 - 8*z^2])*
      (1 + Sqrt[1 - 8*z^2]))/
     (8*z^2*(System`Hypergeome\
tricDump`k +
       System`HypergeometricDu\
mp`k^2 + 2*z^2))) +
   (1/Sqrt[1 - 8*z^2])*
    ((-1 + Sqrt[1 - 8*z^2])*
      PolyGamma[0, 3/4 -
        (1/4)*Sqrt[1 -
           8*z^2]] -
     (-1 + Sqrt[1 - 8*z^2])*
      PolyGamma[0, 5/4 -
        (1/4)*Sqrt[1 -
           8*z^2]] +
     (1 + Sqrt[1 - 8*z^2])*
      (PolyGamma[0, (1/4)*
         (3 + Sqrt[1 -
           8*z^2])] -
       PolyGamma[0, (1/4)*
         (5 + Sqrt[1 -
           8*z^2])]))

• Follow-Ups:
  • Re: Odd result from Sum
    • From: János <janos.lobb@yale.edu>