Re: Series question: limiting total derivative order

• To: mathgroup at smc.vnet.net
• Subject: [mg95196] Re: Series question: limiting total derivative order
• Date: Fri, 9 Jan 2009 06:25:23 -0500 (EST)
• References: <gk3fav\$ds1\$1@smc.vnet.net>

```On Jan 7, 4:54 pm, Bob Hanlon <hanl... at cox.net> wrote:
> Normal[Series[f[x, y], {x, 0, 2}, {y, 0, 2}]] /.
>  Derivative[m_, n_][f][__] /; m + n > 2 :> 0
>
> (1/2)*x^2*Derivative[2, 0][f][0,
>        0] + y*(x*Derivative[1, 1][f][
>             0, 0] + Derivative[0, 1][f][
>           0, 0]) + x*Derivative[1, 0][f][
>        0, 0] + (1/2)*y^2*
>      Derivative[0, 2][f][0, 0] +
>    f[0, 0]
>
> Bob Hanlon
>
> ---- car... 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.

This is compact and elegant, thanks.  My application actually
deals with expanding second-order tensors in 3D (max total derivative
order of 6) but this rule can be applied component-wise.

```

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