Is there a symbol for comparing coefficients?

Question

While doing PFs, ODEs or many other things, comparing coefficients often come up. Is it wrong to use the '=' for comparing coefficients, e.g. '$4x^2$ + 3x = Ax ∴ A=3'. Or is there a correct symbol to use?

Answer 1

We can use the coefficient of operator $[x^n]$ to denote the coefficient of $x^n$ of a series.

This way it follows from the equality \begin{align*} 4x^2+3=Ax \end{align*} the equality \begin{align*} 3=[x]\left(4x^2+3\right)=[x](Ax)=A \end{align*} of the coefficients of $x$.

Note: See for instance formula (5.53) in Concrete Mathematics by R. L. Graham, D. Knuth and O. Patashnik for more information.