Para-Bannai-Ito Polynomials

IF 0.9 3区物理与天体物理 Q2 MATHEMATICS

Symmetry Integrability and Geometry-Methods and Applications Pub Date : 2023-11-10 DOI:10.3842/sigma.2023.090

Jonathan Pelletier, Luc Vinet, Alexei Zhedanov

引用次数: 0

Abstract

New bispectral polynomials orthogonal on a Bannai-Ito bi-lattice (uniform quadri-lattice) are obtained from an unconventional truncation of the untruncated Bannai-Ito and complementary Bannai-Ito polynomials. A complete characterization of the resulting para-Bannai-Ito polynomials is provided, including a three term recurrence relation, a Dunkl-difference equation, an explicit expression in terms of hypergeometric series and an orthogonality relation. They are also derived as a $q\to -1$ limit of the $q$-para-Racah polynomials. A connection to the dual $-1$ Hahn polynomials is also established.

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Para-Bannai-Ito 多项式

通过对未截断的Bannai-Ito多项式和互补的Bannai-Ito多项式的非常规截断，得到了正交于Bannai-Ito双格(一致四格)上的新的双谱多项式。给出了所得到的拟bannai - ito多项式的完整表征，包括一个三项递推关系、一个dunkl -差分方程、一个超几何级数的显式表达式和一个正交关系。它们也被推导为$q$ $-para-Racah多项式的$q$ $到-1$ $的极限。建立了与偶$-1$ Hahn多项式的联系。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Symmetry Integrability and Geometry-Methods and Applications 物理-物理：数学物理

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

4-8 weeks

期刊介绍： Scope Geometrical methods in mathematical physics Lie theory and differential equations Classical and quantum integrable systems Algebraic methods in dynamical systems and chaos Exactly and quasi-exactly solvable models Lie groups and algebras, representation theory Orthogonal polynomials and special functions Integrable probability and stochastic processes Quantum algebras, quantum groups and their representations Symplectic, Poisson and noncommutative geometry Algebraic geometry and its applications Quantum field theories and string/gauge theories Statistical physics and condensed matter physics Quantum gravity and cosmology.

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