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

Out=
-(((-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])]))

```

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