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 -- +-----------------------------------+-----------------------------+ | 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) | +-----------------------------------+-----------------------------+