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How do I write taylor expansion as exponential function?

  1. May 1, 2015 #1
    How do I write taylor expansion of a function of x,y,z (not at origin) as an exponential function?
    Please see the attached image. I need help with the cross terms. I don't know how to include them in the exponential function?

    Attached Files:

  2. jcsd
  3. May 1, 2015 #2


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    Well, [itex]f(x+y) = f(x) + y \frac{d}{dx} f + \frac{y^2}{2} \frac{d^2}{dx^2} f + ...[/itex], which can be formally written as:

    [itex]f(x+y) = e^{y \frac{\partial}{\partial x}} f(x)[/itex]

    or to be more physics-like,

    [itex]f(x+y) = e^{\frac{i}{\hbar} y p_x} f(x)[/itex]

    This is discussed here:
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