Bug with Limit, Series and ProductLog ?

*To*: mathgroup at smc.vnet.net*Subject*: [mg61402] Bug with Limit, Series and ProductLog ?*From*: "did" <didier.oslo at hotmail.com>*Date*: Tue, 18 Oct 2005 02:44:48 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

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.

**Follow-Ups**:**Re: Bug with Limit, Series and ProductLog ?***From:*"Carl K. Woll" <carl@woll2woll.com>

**Re: Bug with Limit, Series and ProductLog ?***From:*"Carl K. Woll" <carl@woll2woll.com>