       Re: Series question: limiting total derivative order

• To: mathgroup at smc.vnet.net
• Subject: [mg95158] Re: [mg95136] Series question: limiting total derivative order
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Wed, 7 Jan 2009 18:54:35 -0500 (EST)

```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

=============
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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