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arXiv · 2604.22616

Skew-orthogonal polynomials for a quartic Freud weight: two classes of quasi-orthogonal polynomials

Costanza Benassi·Marta Dell'Atti
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Abstract

This work is a thorough investigation of skew-orthogonal polynomials with respect to a quartic Freud weight. We provide an explicit method to evaluate skew-orthogonal polynomials of any degree as linear combinations of orthogonal polynomials. The coefficients of these combinations can be evaluated via novel recursive relations. Moreover, we observe that skew-orthogonal polynomials with even and odd degree constitute two families of quasi-orthogonal polynomials with respect to two different semi-classical Laguerre weights, and we provide the first instance of closed recursive relations involving skew-orthogonal polynomials only.

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BibTeXRIS

Costanza Benassi, Marta Dell'Atti. 2026-04-24. Skew-orthogonal polynomials for a quartic Freud weight: two classes of quasi-orthogonal polynomials. https://arxiv.org/abs/2604.22616

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