3rd order, multivariable taylor series

[sandy.bridge]

Homework Statement

Hello all, I have been working on a 3rd order taylor series, but the formula I have does not seem to get me the right answer. The formula I was given is for a taylor polynomial about point (a,b) is:
$$P_3=f(a,b)<br /> +\left( f_{1}(a,b)x+f_{2}(a,b)y\right)$$
$$+\left(\frac1{2}f_{11}(a,b)x^2+f_{12}(a,b)xy +\frac1{2}f_{22}(a,b)y^2\right)$$
$$+\left(\frac1{6}f_{111}(a,b)x^3+\frac1{2}f_{112}(a,b)x^2y +\frac1{2}f_{122}(a,b)xy^2+\frac1{6}f_{222}(a,b)y^3\right)$$

 

[sandy.bridge]

I'm thinking the issue here is all x variable need to be replaced with (x-a), and all y variables need to be replaced with y-b. Can someone clarify this?

 

[SammyS]

Homework Statement

Hello all, I have been working on a 3rd order Taylor series, but the formula I have does not seem to get me the right answer. The formula I was given is for a taylor polynomial about point (a,b) is:
$$P_3=f(a,b)<br /> +\left( f_{1}(a,b)x+f_{2}(a,b)y\right)$$
$$+\left(\frac1{2}f_{11}(a,b)x^2+f_{12}(a,b)xy +\frac1{2}f_{22}(a,b)y^2\right)$$
$$+\left(\frac1{6}f_{111}(a,b)x^3+\frac1{2}f_{112}(a,b)x^2y +\frac1{2}f_{122}(a,b)xy^2+\frac1{6}f_{222}(a,b)y^3\right)$$

Wherever you have x in that formula, replace it with (x-a).

Wherever you have y in that formula, replace it with (y-b).

 

[sandy.bridge]

Thanks a lot!