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MathGroup Archive 1999

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Zeta Function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg20556] Zeta Function
  • From: Andre Heinemann <A.Heinemann at ifw-dresden.de>
  • Date: Sat, 30 Oct 1999 00:14:06 -0400
  • Sender: owner-wri-mathgroup at wolfram.com

In Mathematica 2.2 and 4.0 a friend
pushed me to the following
problem. And for me it is a bug
in Mathematica because we solved it
with Mapple in the right way.

At x== 1 the zeta function has a 1/(x -1)
singular point as you can see in a plot.
So the Series[D[Zeta[x],x],{x,1,2}]
should have the leading term of -1/(x-1)^2.
But it hasn't !

Only in the D[Series[Zeta[x], {x, 1, 2}], x]
expression I can find this leading part.

I made a test with a other singular point,
the x == -1 for Gamma[x].

The leading terms of

D[ Series[Gamma[x], {x, -1, 1}], x]

and 

Series[D[Gamma[x], x], {x, -1, 1}]

are both of the type 1/(1+x)^2 as one expect.

But what is wrong with the Zeta function ???

And by the way, Plot[Normal[Series[Zeta[x],{x,1,2}]],{x,0,2}]
doesn't work and I can't see why not ?
Can you help me ?
  
Regards,

Andre 
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