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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)
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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



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