All poles lie outside some circle $|z|=R$ with $R>1$. The <rational function> is <holomorphic> in that disc, so its <Taylor series> at zero <converges uniformly> on $|z|\le1$. Its <polynomial> <partial sums> therefore approximate uniformly on $K$. If there are no finite poles, the function is already a <polynomial>.

Solution

Past exam of the mathematics course of the University of Cambridge / 2006 / ii / Paper 2 / 11G / a / Solution

 Solution (source code)