Multidimensional extension of the Taylor series in Mathematica

Question

Mathematica seems to lack a function for this, or I still can't find it.

A function Seriescan sequentially perform an extension for several variables, but it seems it cannot perform a full multidimensional extension.

Does anyone know how to do this?

thank

Answer 1

This question is not clear to me. You mean something like this, where do you get conditions to a certain certain extent?

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