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Iterated integrals and Borwein-Chen-Dilcher polynomials. (English) Zbl 1481.33009

Summary: 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 \((2\alpha +1)/2\), \(\alpha \in \mathbb{Z}_+\).

MSC:

33C47 Other special orthogonal polynomials and functions
30C10 Polynomials and rational functions of one complex variable
30C15 Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral)
30E15 Asymptotic representations in the complex plane
42C05 Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis
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