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Re: Series question: limiting total derivative order

  • To: mathgroup at smc.vnet.net
  • Subject: [mg95148] Re: Series question: limiting total derivative order
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Wed, 7 Jan 2009 07:11:37 -0500 (EST)
  • Organization: Uni Leipzig
  • References: <gk1rod$ouc$1@smc.vnet.net>
  • Reply-to: kuska at informatik.uni-leipzig.de

Hi,

Normal[Series[f[x, y], {x, 0, 2}, {y, 0, 2}]] /.
  Derivative[dlst__][f][args__] /; Plus[dlst] > 2 :> 0

Regards
   Jens

carlos at colorado.edu wrote:
> Is it possible to directly tell Series to truncate a
> multivariate Taylor series beyond a total derivative order?
> Example, for f(x,y) and total derivative order 2, I want
> 
>      f(0,0) + x*Derivative[1,0][f][0,0] +  y*Derivative[0,1][f][0,0] +
>      x^2*Derivative[2,0][f][0,0]/2 +  x*y*Derivative[1,1][f][0,0] +
>      y^2*Derivative[0,2][f][0,0]/2
> 
> whereas
> 
>     Normal[Series[f[x,y],{x,0,2},{y,0,2}]]
> 
> returns also derivative terms (2,1), (1,2) and (2,2) of total
> orders 3, 3 and 4.  These I have to get rid of a posteriori with
> some complicated logic to build a replacement list.
> 


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