1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

I Coefficients in a quotient of sums

  1. Feb 7, 2017 #1
    Is there a general way to express, for instance, the coefficient of the order $x^j$ term in the expression

    $$\frac{\Sigma_{n}^{\infty}a_nx^n}{\Sigma_{m}^{\infty}b_mx^m}$$ ?

    Basically I am working with a quotient of two infinite power series and I want to know the term in this quotient that is proportional to a particular power of the expansion variable. Am I even guaranteed that there will be such a term? How do I find it?
  2. jcsd
  3. Feb 8, 2017 #2

    Stephen Tashi

    User Avatar
    Science Advisor

    You could try doing division, similar to the way that one divides one polynomial by another polynomial. There's an example on page 3 of http://www2.fiu.edu/~aladrog/IntrodPowerSeries.pdf
  4. Feb 8, 2017 #3
    That was a bit tedious, but I think it actually worked for my purpose. Thanks!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted