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arXiv · 2305.03370

More properties of $(\beta,\gamma)$-Chebyshev functions and points

Stefano De Marchi·Giacomo Elefante·Francesco Marchetti·Jean-Zacharie Mariethoz
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Abstract

Recently, $(\beta,\gamma)$-Chebyshev functions, as well as the corresponding zeros, have been introduced as a generalization of classical Chebyshev polynomials of the first kind and related roots. They consist of a family of orthogonal functions on a subset of $[-1,1]$, which indeed satisfies a three-term recurrence formula. In this paper we present further properties, which are proven to comply with various results about classical orthogonal polynomials. In addition, we prove a conjecture concerning the Lebesgue constant's behavior related to the roots of $(\beta,\gamma)$-Chebyshev functions in the corresponding orthogonality interval.

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Stefano De Marchi, Giacomo Elefante, Francesco Marchetti, Jean-Zacharie Mariethoz. 2023-05-05. More properties of $(\beta,\gamma)$-Chebyshev functions and points. https://arxiv.org/abs/2305.03370

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