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3rd order, multivariable taylor series

  1. Dec 6, 2011 #1
    1. The problem statement, all variables and given/known data
    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:
    [tex]P_3=f(a,b)
    +\left( f_{1}(a,b)x+f_{2}(a,b)y\right) [/tex]
    [tex]+\left(\frac1{2}f_{11}(a,b)x^2+f_{12}(a,b)xy +\frac1{2}f_{22}(a,b)y^2\right)[/tex]
    [tex]+\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)[/tex]
     
  2. jcsd
  3. Dec 6, 2011 #2
    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?
     
  4. Dec 6, 2011 #3

    SammyS

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

    Wherever you have y in that formula, replace it with (y-b).
     
  5. Dec 6, 2011 #4
    Thanks a lot!
     
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