Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Multiplication of Maclaurin Series

  1. Aug 16, 2008 #1
    I have the following problem:

    find the first 3 non-zero terms in the Maclaurin series for the function:

    e-x2 + Cos[x]

    I know in this case, the series behave like polynomials and I have done the following. The left expression is the first 3 terms of the e portion of the problem, and the second expression is the first 3 terms of Cosx.

    (1 - x2+ x4/2)(1 - x2/2 + x4/24)

    this =

    1 - x2/2 + x4/24 - x2 - x4/2 - x6/24 + x4 - x6/4 + x8/48

    How do I know which terms are the "first 3 non-zero terms" of this series?

    Thanks - the answer is attached, I just don't understand how the polynomial, after multiplied out is consolidated at the end.

    Jeff power series multiplication answer.jpg
  2. jcsd
  3. Aug 16, 2008 #2


    User Avatar
    Science Advisor
    Homework Helper

    Hi Jeff! :smile:

    (You meant e-x2 *Cos[x] :wink:)

    The "first three terms" would be 1 + 0.x - x2/2 .

    "non-zero" simply means that you skip over "0.x" and "0.x3" :smile:
    You can always change the order of the terms of a series (except if you're using an infinite number of terms, in which case there are rules to follow :wink:).
  4. Aug 16, 2008 #3

    Thanks, and yes - not sure how "+" found its way in there :-)

    2 Questions -

    What is "0.x" and since the 2 original series are infinite, isn't the product of the series infinite as well?

    So, just to confirm: If I take the first 3 terms of each Taylor polynomial and multiply through (line 4 in the image), I can use any 3 non zero terms of that product? What convention compelled them to use:

    1 - 1.5x2 +25/24x4 as the answer to the question?

    Many Thanks,

  5. Aug 16, 2008 #4


    User Avatar
    Science Advisor
    Homework Helper

    I meant 0 times x.

    Yes, it is infinite, but you're only using a few terms at the beginning.
    Nooo … you must use all the terms of the three lowest powers (x0 x2 and x4).

    Those are the "first 3 non-zero terms". :smile:
  6. Aug 16, 2008 #5
    Great - that clarifies it perfectly. Thanks for your help, Tim.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook