Series expansion of Lambert series

*To*: mathgroup at smc.vnet.net*Subject*: [mg127979] Series expansion of Lambert series*From*: "Dr. Wolfgang Hintze" <weh at snafu.de>*Date*: Fri, 7 Sep 2012 04:54:49 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net

Define for 0<=x<1 the Lambert series f[x_] := Sum[ x^n/(1-x^n), {x,1,oo}] How do I get Mathematica to calculate the first few terms of a series expansion like Series[f[x],{x,0,4}] ? Also a series like e1[x_] := Sum[x^n/(1+n!), {n,0,oo}] does not seem to be expandable with Series. BTW same thing in 8.0 and 5.2 Regards, Wolfgang

**Follow-Ups**:**Re: Series expansion of Lambert series***From:*michael partensky <partensky@gmail.com>

**Re: Series expansion of Lambert series***From:*Bob Hanlon <hanlonr357@gmail.com>