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Re: convert an expression to an infinite series

• To: mathgroup at smc.vnet.net
• Subject: [mg29638] Re: [mg29618] convert an expression to an infinite series
• From: Daniel Lichtblau <danl at wolfram.com>
• Date: Fri, 29 Jun 2001 01:36:12 -0400 (EDT)
• References: <200106280928.FAA06752@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

"Toshiyuki (Toshi) Meshii" wrote:
> 
> Hello,
> 
> Does anyone know a way to convert an expression to an infinite series?
> Let me show the idea by a concrete problem.
> 
> In[29]:=
> Sum[E^(-2*m*n*L), {n, 0, Infinity}]
> 
> Out[29]=
> E^(2*L*m)/(-1 + E^(2*L*m))
> 
> Yes, Mathematica 4.1 knows that the infinite sum converges to a specific
> value.
> Then, my question is that how can I expand the expression
>  E^(2*L*m)/(-1 + E^(2*L*m))
> in an infinite series on n, in this case
>  Sum[E^(-2*m*n*L), {n, 0, Infinity}]
> 
> Is there any way or is it an one way path?
> 
> -Toshi


Something along these lines was recently raised in this news group. See

http://library.wolfram.com/mathgroup/archive/2001/Apr/msg00245.html

and the various responses. In particular

http://library.wolfram.com/mathgroup/archive/2001/Apr/msg00270.html

may help to clarify why this is not possible in any way that is both
simple and general.


Daniel Lichtblau
Wolfram Research

• References:
  • convert an expression to an infinite series
    • From: "Toshiyuki \(Toshi\) Meshii" <meshii@mech.fukui-u.ac.jp>