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Termwise multiplication

  1. Nov 22, 2005 #1
    for a termwise mulitiplication of two taylor series,
    1.sigma a m(x-x0)^m
    2.sigma b m (x-x0)^m
    then if you mutilpy 1 and 2, shouldn't you get
    sigma a mbm(x-x0)^2m?
    but my textbook says that it's only
    sigma a mbm(x-x0)^m

    from advanced engineering mathematics by erwin kreyszig 9E pg202
     
  2. jcsd
  3. Nov 22, 2005 #2

    EnumaElish

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    For termwise multiplication [itex]a_m b_m (x - x_0)^{2m}[/itex] is right.

    If you were adding the two together then [itex](a_m + b_m)(x - x_0)^{m}[/itex] would have been right.

    On the other hand, it just may be possible that your textbook defines termwise Taylor series multiplication as [itex]a_m b_m (x - x_0)^{m}[/itex]. In which case it would be right on its own accord.
     
    Last edited: Nov 22, 2005
  4. Nov 22, 2005 #3

    matt grime

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    It would certainly appear to be the definition that you're having trouble with. Ie, that is the definition of termwise mult. I can see why it is morally wrong to think it a_mb_m(x-x_0)^2m

    since you should be thinking of the x-x_0 part merely as a place holder.

    Thus a taylor series is really a sequence (a_m) m in N, and addition and multiplication of the series is done as for the sequences.
     
  5. Nov 23, 2005 #4
    thank you very much!!! :)
     
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