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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