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