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Basic taylor series for f(x-dx)

  1. Feb 13, 2010 #1
    Hi, how would you find the taylor series for f(x-dx). i know that substituting x-dx in the series for f(x) is not correct.
     
  2. jcsd
  3. Feb 13, 2010 #2

    mathman

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    You are using an unusual terminology. Typically a Taylor series looks like:

    f(a+x)=f(a) + xf'(a) + x2 f''(a)/2! + ...

    When a=0, it is called a MacLaurin series.
     
  4. Feb 13, 2010 #3
    what happens if you have dx instead of a. the second post on this website http://www.wilmott.com/messageview.cfm?catid=19&threadid=17563 [Broken]
    has a formula but i dont know how it was derived.
     
    Last edited by a moderator: May 4, 2017
  5. Feb 13, 2010 #4
    u are using dx in the sense of a second point of x, or a change in x
    check out this page from wikiversity that breaks everything down really well.
    normally i know that posts from wiki are frowned upon, but i learnt from this site and i think they break it down really rigorously and guide you nicely through the expansion of a function into a summed power series and then into taylors series at different points.
    http://en.wikiversity.org/wiki/Taylor's_series
     
  6. Feb 14, 2010 #5
    Saying "Taylor Series" is not enough, you have to attach a point around which you are expanding the function. Notice that around a different point, the taylor series will also have different coefficients.

    In your example, f(x+dx) was calculated around a point x, so of course substitution won't work for the exapnasion of f(x) around 0.
     
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