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

中文翻译：

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迭代积分和Borwein-Chen-Dilcher多项式

我们研究了多项式的迭代积分的零位置和渐近行为。Borwein-Chen-Dilcher的多项式在这个问题上起着重要的作用。对于这些多项式，我们发现它们的渐近性很强，并给出了零分布的极限度量。我们应用这些结果来描述参数\（（2 \ alpha +1）/ 2 \），\（\ alpha \ in \ mathbb {Z} _ {+} \）中的超球形多项式的迭代积分的零渐近分布。