The bernsteim polynomial in one variable

Abstract

The lemma on b-functions is a result due to I.N.Bernstein about the existence of certain differential operators with polynomial coefficients.In this paper we give an elementary and constructive proof of this result that works well in one variable.Our method results in a simple formula for the Bernstein polynomial b(λ)and a recursive definition for a differential operator d(λ)that produces b(λ).As an application we consider two consequences about the poles of certain meromorphic functions defined by the analytic continuation of distributions.