       Re: Series expansion of Lambert series

• To: mathgroup at smc.vnet.net
• 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)
• 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: <20120907085449.BF69F6790@smc.vnet.net>

```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

As to Eq. (2), try this:

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

Out= {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
>
>

```

• Prev by Date: Re: Series expansion of Lambert series
• Next by Date: Re: Count inside a matrix?
• Previous by thread: Re: Series expansion of Lambert series
• Next by thread: Re: Series expansion of Lambert series