Asymptotic Normality of the Coefficients of the Morgan-Voyce Polynomials

Moussa Benoumhani; Bernhard Heim; Markus Neuhauser

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arXiv · 2204.11237

Asymptotic Normality of the Coefficients of the Morgan-Voyce Polynomials

Moussa Benoumhani·Bernhard Heim·Markus Neuhauser

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Abstract

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

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Moussa Benoumhani, Bernhard Heim, Markus Neuhauser. 2022-04-24. Asymptotic Normality of the Coefficients of the Morgan-Voyce Polynomials. https://arxiv.org/abs/2204.11237

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