The single-indexed exceptional Krawtchouk polynomials

Mikami, Hiroshi; Tsujimoto, Satoshi; Vinet, Luc

doi:10.48550/arxiv.2201.12359

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2023

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“…In García-Ferrero et al, 24 a complete classification of the continuous XOP which generalizes the classical ones (Jacobi, Laguerre, and Hermite polynomials) was addressed. One can also refer to Miki et al 25 for a detailed discussion of the exceptional Krawtchouk polynomials.…”

Section: Introductionmentioning

confidence: 99%

Exceptional Laurent biorthogonal polynomials through spectral transformations of generalized eigenvalue problems

Luo

Tsujimoto

2023

Stud Appl Math

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A formulation is given for the spectral transformation of the generalized eigenvalue problem through the decomposition of the second-order differential operators. This allows us to construct some Laurent biorthogonal polynomial systems with gaps in the degree of the polynomial sequence. These correspond to an exceptionaltype extension of the orthogonal polynomials, as an extension of the Laurent biorthogonal polynomials. Specifically, we construct the exceptional extension of the Hendriksen-van Rossum polynomials, which are biorthogonal analogs of the classical orthogonal polynomials. Similar to the cases of exceptional extensions of classical orthogonal polynomials, both state-deletion and state-addition occur.

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Section: Introductionmentioning

confidence: 99%