Mathematica seems to be missing a function for this, or I can't find it anyway.
The Series function can do expansion in succession for multiple variables, but it doesn't seem capable of doing a full multivariate expansion.
Does anyone know how to do this?
Thanks
This question is not clear to me. Do you mean something like this, where you get terms up to some specified total degree?
f[x_, y_] := Sin[x*y^2] + x^4*y - 3*x*Cos[y] - x^2*y^3
Normal[Series[f[x*t, y*t], {t, 0, 5}]] /. t -> 1
(*
-> -3*x + x^4*y + (5*x*y^2)/2 - x^2*y^3 - (x*y^4)/8
*)
Daniel Lichtblau