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Taylor series

  1. Oct 8, 2006 #1
    Let be an analytic function f(x,y) so we want to take its Taylor series, my question is if we can do this:

    -First we expand f(x,y) on powers of y considering x a constant so:

    [tex] f(x,y)= \sum_{n=0}^{\infty}a_{n} (x)y^{n} [/tex]

    and then we expand a(n,x) for every n into powers of x so we have..

    [tex] f(x,y)= \sum_{n=0}^{\infty}\sum_{m=0}^{\infty}b_{n}x^{m} y^{n} [/tex]

    I don't know if the result will be the same that taking the "Double Taylor series " for the function f(x,y) :confused: :confused: :confused:
  2. jcsd
  3. Oct 8, 2006 #2

    matt grime

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    b_n should be b_m, and you're just asking about when you can reorder summation which is a well known property of certain sums, and not others.
  4. Oct 8, 2006 #3


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    bn should be bn,m.
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