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Re: Series and passing a function a changing number of variables

  • To: mathgroup at smc.vnet.net
  • Subject: [mg106824] Re: Series and passing a function a changing number of variables
  • From: Albert Retey <awnl at gmx-topmail.de>
  • Date: Sun, 24 Jan 2010 05:42:10 -0500 (EST)
  • References: <hjeq32$fjd$1@smc.vnet.net>

Am 23.01.2010 13:29, schrieb Ignacio Plazeta:
> Dear Friends
> 
> -- 1 -----------------------------------------------
> 
> This command works fine:
> 
> Series[ Exp[ x + 2 y^x ] , {x, 0, 2} ,  {y, 0, 2} ]
> 
> this one doesn't:
> 
> Series[ Exp[ x + 2 y^x ] ,  {{x, 0, 2}, {y, 0, 2}} ]
> 
> It returns:
> 
> "Series specification is not a list with three elements ..."
> 
> -- 2 -----------------------------------------------
> 
> I'm trying to set up this kind of function:
> 
> myTaylorExpander[ function_ , varList , startPoint_ , ord_ ]
> 
> where varList length is changing; because of the above mentioned
> behavior of Series function I can't simply try something like:
> 
> numVar = Length[ varList ];
> 
> args = Table[
> 
> { varList[[k]] , startPoint , ord}
> 
> , { k, 1 , numVar }
> 
> ]
> 
> Series[ f , args ] // Normal
> 
> -- 3 -----------------------------------------------
> 
> Is there a way to get out of this by a trick to pass a functions
> a changing number of variable ? Anything else fitting is welcomed too.

What you are looking for is Sequence, see the code below:

varList = {x, y, z};

numVar = Length[varList]

startPoint = 0; ord = 2;

args = Apply[Sequence,Table[{varList[[k]], startPoint, ord}, {k, 1,
numVar}]]

Series[f[x, y, z], args] // Normal

note that you will get more replies when you provide a working example
with which people can play around...

hth,

albert


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