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Series question: limiting total derivative order


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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