# Wilkinson Polynomials

This article is about a family of polynomials introduced by James H. Wilkinson some five decades ago, which have the peculiar property that some of their zeros are extremely sensitive to small changes in the values of one or more of the coefficients.

If $n$ is a non-negative integer, we define the Wilkinson polynomials $W(x,n)$ by

$$W(x,0) = 1$$
$$(x,1) = x-1$$
$$W(x,2) = (x-2)(x-1)$$
$$(x,3) = (x-3)(x-2)(x-1)$$

and so on to give $$W(x,n) = (x-n) W(x,n-1) \quad \mbox{for} \quad n>0.$$