Description: Complex numbers and complex-valued functions; differentiation of complex functions; power series, uniform convergence; integration, contour integrals; elementary conformal mapping. Not ...

For a power series $f(z) = \sum^\infty_{k = 0} a_kz^k$ let $S_n(f)$ denote the maximum modulus of the zeros of the $n$th partial sum of $f$ and let $r_n(f)$ denote ...