Series question: limiting total derivative order

*To*: mathgroup at smc.vnet.net*Subject*: [mg95136] Series question: limiting total derivative order*From*: carlos at colorado.edu*Date*: Wed, 7 Jan 2009 04:12:42 -0500 (EST)

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.