Coefficients in a quotient of sums

[Sturk200]

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?

 

[Stephen Tashi]

Is there a general way to express, for instance, the coefficient of the order $x^j$ term in the expression

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

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

 

[Sturk200]

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

That was a bit tedious, but I think it actually worked for my purpose. Thanks!