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Re: Series expansion of Lambert series

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  • Subject: [mg128014] Re: Series expansion of Lambert series
  • From: michael partensky <partensky at gmail.com>
  • Date: Sat, 8 Sep 2012 03:12:28 -0400 (EDT)
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Hi, Wolfgang.
The first definition seems ambiguous.
(1) x in (1) is a "silent" variable (summation index), and  can not appear
in the left side.
(2) x=1 leads to divergence (~\inf). And it's contradict the allowed range
of x.
(3) Apparently, the summation index is n, in which case the next comment
can be helpful.

As to Eq. (2), try this:

e1[x_] := NSum[x^n/(1 + Factorial[n]), {n, 0, \[Infinity]}];
In[12]:= Table[e1[x], {x, 1, 10}]

Out[12]= {1.52607, 5.00291, 15.7894, 47.4019, 136.98, 385.988, \
1070.88, 2943.92, 8050.98, 21954.5}

Hope it helps.
Best.
Michael Partenskii
olfgang Hintze <weh at snafu.de> wrote:

> Define for 0<=x<1 the Lambert series
>
> f[x_] := Sum[ x^n/(1-x^n), {x,1,oo}]  *(1)*
>
> 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}] * (2)*
>
> does not seem to be expandable with Series.
>
> BTW same thing in 8.0 and 5.2
>
> Regards,
> Wolfgang
>
>




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