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
|
| How can I workaround the problem and get the
correct
| expansion for In[3]?
| Thanks,
| D.
|

```

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