Iterated Integrals and Borwein–Chen–Dilcher Polynomials

Abstract

We study the zero location and the asymptotic behavior of iterated integrals of polynomials. Borwein–Chen–Dilcher’s polynomials play an important role in this issue. For these polynomials we find their strong asymptotics and give the limit measure of their zero distribution. We apply these results to describe the zero asymptotic distribution of iterated integrals of ultraspherical polynomials with parameters $$(2\alpha +1)/2$$ , $$\alpha \in \mathbb {Z}_{+}$$ .