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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

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    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!
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