       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].

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
--
+-----------------------------------+-----------------------------+
| mobil tel.    0177  26 92 103     |  Andre Heinemann            |
| priv. tel.   (0351) 25 23 574     |  Institut fuer Festkoerper- |
| Tel.: (++49) (351) 4659 - 686     |  und Werkstofforschung      |
| Fax:  (++49) (351) 4659 - 452     |  Helmholtzstr. 20, R2.140   |
| email: a.heinemann at ifw-dresden.de |  Postfach 27 00 16          |
|                                   |  D-01171 Dresden (Germany)  |
+-----------------------------------+-----------------------------+

```