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arXiv · 2606.06639

Quasi-Orthogonal Polynomials and Exceptional Sequences

Rachel Bailey·Roman Gavrilov
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Abstract

Motivated by recent developments in Exceptional Orthogonal Polynomials (XOPs), which feature sequences of orthogonal polynomials missing finitely many degrees, we develop a construction of monic orthogonal polynomial sequences that omit a single degree using linear combinations of classical families. We then relate these polynomial families to quasi-orthogonal polynomials of order 2.

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Rachel Bailey, Roman Gavrilov. 2026-06-04. Quasi-Orthogonal Polynomials and Exceptional Sequences. https://arxiv.org/abs/2606.06639

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