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Re: Series and passing a function a changing number of

  • To: mathgroup at smc.vnet.net
  • Subject: [mg106831] Re: [mg106758] Series and passing a function a changing number of
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Sun, 24 Jan 2010 05:43:31 -0500 (EST)
  • Reply-to: hanlonr at cox.net

f[x_] = Exp[x + 2 y^x];

varList = Cases[f[x],
   _Symbol?(! NumericQ[#] &), Infinity] // Union

{x,y}

startPoint = 0;

ord = 2;

args = {#, startPoint, ord} & /@ varList;

Or you could use Thread

args == Thread[{varList, startPoint, ord}]

True

Convert the args list to a sequence for use in Series

Series[f[x], Sequence @@ args] // Normal

x^2*(3*E^2*Log[y]^2 + 2*E^2*Log[y] + E^2/2) + 
   x*(2*E^2*Log[y] + E^2) + E^2

% // FullSimplify

(1/2)*E^2*(2*x*Log[y]*(3*x*Log[y] + 2*x + 2) + x*(x + 2) + 
      2)


Bob Hanlon

---- Ignacio Plazeta <Ignacio.Plazeta at speednet.es> wrote: 

=============
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.

Warmest Regards.

Ignacio Plazeta
( Spain )



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