Re: Bug with Limit, Series and ProductLog ?
- To: mathgroup at smc.vnet.net
- Subject: [mg61465] Re: Bug with Limit, Series and ProductLog ?
- From: "Jens-Peer Kuska" <kuska at informatik.uni-leipzig.de>
- Date: Wed, 19 Oct 2005 02:17:31 -0400 (EDT)
- Organization: Uni Leipzig
- References: <dj26kc$bc7$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Hi, and the essential singularity at x==0 of ProductLog[Exp[a/x]/x]-a/x does not matter ? Regards Jens "did" <didier.oslo at hotmail.com> schrieb im Newsbeitrag news:dj26kc$bc7$1 at smc.vnet.net... | With Mathematica 5.2 Windows I obtain | | In[1]:=Limit[ ProductLog[Exp[a/x]/x]-a/x,x->0] | Out[1]= -Log[a] | | which seems correct. But, setting a=1, I get | | In[2]:=Limit[ ProductLog[Exp[1/x]/x]-1/x,x->0] | Out[2]=-8 | | which is inconsistent with the previous result | (except if Log[1] is Infinity !). | | Worse, with Series I get | | In[3]:=Series[ ProductLog[Exp[a/x]/x]-a/x,{x,0,5}] | | Out[3]=\!\(\* | InterpretationBox[ | RowBox[{\(-\(a\/x\)\), "+", "Indeterminate", "+", | InterpretationBox[\(O[x]\^6\), | SeriesData[ x, 0, {}, -1, 6, 1], | Editable->False]}], | SeriesData[ x, 0, { | Times[ -1, a], Indeterminate}, -1, 6, 1], | Editable->False]\) | | Setting a=1 in the Series gives a complex answer. | | How can I workaround the problem and get the correct | expansion for In[3]? | Thanks, | D. |