# taylor series several variable representation and CoefficientList [closed]

I like to do the following; but the representation as sum it does not match with the taylor series how could it be done?? Thanks in advance

• You mistakenly used only one index in the powers of x and y in the sum. Feb 26 at 21:31
• @BobHanlon (+1) for the comment and sorry. I just saw your comment as I edited the answer. I am happy to delete mine if you would like to write one.
– kcr
Feb 26 at 21:34
• @DiSp0sablE_H3r0 - Don't worry about it. Feb 26 at 21:36

You need to use two distinct indices in the sums.

srs = Normal[Series[ArcSin[x + y]^2, {x, 0, 3}, {y, 0, 3}]] // Expand;
g = CoefficientList[srs, {x, y}];

Sum[g[[k + 1, j + 1]] x^k y^j, {k, 0, 3}, {j, 0, 3}]


which gives back

x^2 + 2 x y + (4 x^3 y)/3 + y^2 + 2 x^2 y^2 + (4 x y^3)/3 + (
32 x^3 y^3)/9


Maybe

ser = Series[ArcSin[x + y]^2, {x, 0, 3}, {y, 0, 3}] // Normal // Expand

g = CoefficientList[ser, {x, y}, 4]

(* {{0, 0, 1, 0}, {0, 2, 0, 4/3}, {1, 0, 2, 0}, {0, 4/3, 0, 32/9}} *)