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Power series

  1. May 8, 2005 #1

    quasar987

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    If I evaluate the power serie

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

    at x = 0, the first term is [itex]a_0(0)^0[/itex]. But 0^0 is undefined, is it not? How is this paradox solved?
     
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  3. May 8, 2005 #2

    Hurkyl

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    Because that notation for power series doesn't really mean you're supposed to compute 0^0 to get the n=0 term.

    Though, some sources will prefer to write that series as

    [tex]y(x) = a_0 + \sum_{n=1}^{\infty}a_nx^n[/tex]

    to remove any confusion. (The two mean the same thing, though)
     
    Last edited: May 8, 2005
  4. May 8, 2005 #3

    quasar987

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    I didn't know that. They don't tell us about any of the subtelties of anything at school. They're totally useless.
     
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