ASYMPTOTIC NORMALITY OF THE COEFFICIENTS OF THE MORGAN-VOYCE POLYNOMIALS

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2024年4月1日

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Moussa Benoumhani,
Bernhard Heim,
Markus Neuhauser

摘要

We study arithmetic and asymptotic properties of polynomials provided by $Q_n(x):= x \sum _{k=1}^n k \, Q_{n-k}(x)$ $Q_{n} (x) : = x \sum_{k = 1}^{n} k Q_{n - k} (x)$ with initial value $Q_0(x)=1$ $Q_{0} (x) = 1$ . The coefficients satisfy a central limit theorem and a local limit theorem involving Fibonacci numbers. We apply the methods of Berry and Esseen, Harper, Bender, and Canfield.