Re: Series question: limiting total derivative order

*To*: mathgroup at smc.vnet.net*Subject*: [mg95196] Re: Series question: limiting total derivative order*From*: carlos at colorado.edu*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.