Re: Series expansion of Lambert series

*To*: mathgroup at smc.vnet.net*Subject*: [mg128011] Re: Series expansion of Lambert series*From*: "danl at wolfram.com" <daniel.lichtblau0 at gmail.com>*Date*: Sat, 8 Sep 2012 03:11:28 -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*References*: <k2ccpn$f0g$1@smc.vnet.net>

On Friday, September 7, 2012 3:56:27 AM UTC-5, Dr. Wolfgang Hintze wrote: > 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 Use the fact that you only need n terms of the sum (in these specific examples) in order to obtain n terms of the series expansion. In[17]:= seriesLambert[x_,n_] := Series[Sum[x^k/(1-x^k),{k,n}], {x,0,n}] In[18]:= seriesLambert[x,4] 2 3 4 5 Out[18]= x + 2 x + 2 x + 3 x + O[x] Daniel Lichtblau Wolfram Research