A sequence of polynomials for studying production functions

In this paper, we study a sequence of polynomials, A1(z),A2(z),… useful in the study of production functions. The sequence {An(z)} is given by We present a closed (although not completely transparent) formula for the An(z) and study convergence properties of An(z). We shall also make some calculations of An(λ) for roots of unity λ, and study the limiting behavior of An(z) as n goes to infinity.