       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>

```Hi,

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

Regards
Jens

> 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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