Exercises
[1KS]Prerequisites:[1K7].Difficulty:*.Let \(g(z)=β_{m=0}^β b_ m z^ m\) with \(b_ 0=g(0)β 0\). Express formally the reciprocal function \(f(x)=1/g(x)\) as a power series and calculate the coefficients starting from the coefficients \(b_ m\). If the radius of convergence of \(g\) is non-zero show that the radius of convergence of \(f\) is non-zero and that \(f(x)=1/g(x)\) where the two series \(f(x),g(x)\) converge.
Solution 1