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Our results include proof of the distinct-real-rootedness of every such polynomial $W_n(x)$, derivation of the best bound for the zero-set $\\{x\\mid W_n(x)=0\\ \\text{for some $n\\ge1$}\\}$, and determination of three precise limit points of this zero-set. 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Wang, J.L. Gross, T. Mansour, T.W. Tucker","submitted_at":"2015-01-25T02:35:42Z","abstract_excerpt":"This paper is concerned with the distribution in the complex plane of the roots of a polynomial sequence $\\{W_n(x)\\}_{n\\ge0}$ given by a recursion $W_n(x)=aW_{n-1}(x)+(bx+c)W_{n-2}(x)$, with $W_0(x)=1$ and $W_1(x)=t(x-r)$, where $a>0$, $b>0$, and $c,t,r\\in\\mathbb{R}$. Our results include proof of the distinct-real-rootedness of every such polynomial $W_n(x)$, derivation of the best bound for the zero-set $\\{x\\mid W_n(x)=0\\ \\text{for some $n\\ge1$}\\}$, and determination of three precise limit points of this zero-set. 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