A "missing" family of classical orthogonal polynomials

Abstract

We study a family of "classical" orthogonal polynomials which satisfy (apart from a 3-term recurrence relation) an eigenvalue problem with a differential operator of Dunkl-type. These polynomials can be obtained from the little $q$-Jacobi polynomials in the limit $q=-1$. We also show that these polynomials provide a nontrivial realization of the Askey-Wilson algebra for $q=-1$.

20 pages

References in corpus (2)

• Double Affine Hecke Algebras of Rank 1 and the $Z_3$-Symmetric Askey-Wilson Relations
• The factorization method, self-similar potentials and quantum algebras

Cited by in corpus (104)

• The Liver Tumor Segmentation Benchmark (LiTS)
• SDSS IV MaNGA - Spatially resolved diagnostic diagrams: A proof that many galaxies are LIERs
• A Comparative Survey of Recent Natural Language Interfaces for Databases
• Learning a local Hamiltonian from local measurements
• Using social network and semantic analysis to analyze online travel forums and forecast tourism demand
• Epithelium segmentation using deep learning in H&E-stained prostate specimens with immunohistochemistry as reference standard
• Equilibrium mechanisms of self-limiting assembly
• Exciton diffusion in monolayer semiconductors with suppressed disorder
• Heart Rate Variability as a Predictive Biomarker of Thermal Comfort
• Electrodeposition of Ni-P composite coatings: A review
• The Dunkl oscillator in the plane II : representations of the symmetry algebra
• The X-shooter GRB afterglow legacy sample (XS-GRB)
• How to measure the entropy of a mesoscopic system via thermoelectric transport
• Evaluation of matrix factorisation approaches for muscle synergy extraction
• Towards Safer Smart Contracts: A Survey of Languages and Verification Methods
• The Universal Askey-Wilson Algebra
• XY magnetism, Kitaev exchange, and long-range frustration in the $J_{\mathrm{eff}}=1/2$ honeycomb cobaltates
• Robo-Taxi service fleet sizing: assessing the impact of user trust and willingness-to-use
• Hamiltonian Learning for Quantum Error Correction
• Deeply decarbonizing residential and urban central districts through photovoltaics plus electric vehicle applications
• Deep Learning Approach on Information Diffusion in Heterogeneous Networks
• Topological portraits of multiscale coordination dynamics
• How collective asperity detachments nucleate slip at frictional interfaces
• Multiple relaxation times in single-molecule magnets
• Joint growth rate measurements from redshift-space distortions and peculiar velocities in the 6dF Galaxy Survey
• Impact of Service Sector Loads on Renewable Resource Integration
• The host galaxy of the short GRB111117A at $z=2.211$: impact on the short GRB redshift distribution and progenitor channels
• Boundary states with elevated critical temperatures in Bardeen-Cooper-Schrieffer superconductors
• Bispectrality of the Complementary Bannai-Ito Polynomials
• Developing a self-consistent AGB wind model: II. Non-classical, non-equilibrium polymer nucleation in a chemical mixture
• Collective gradient sensing in fish schools
• Twisted Quantum Double Model of Topological Orders with Boundaries
• The Bannai-Ito algebra and some applications
• Supersymmetric Quantum Mechanics with Reflections
• Unsupervised Classification of Variable Stars
• Fermion Condensation and Gapped Domain Walls in Topological Orders
• Impact of Substrate on Tip-enhanced Raman Spectroscopy --- A Comparison of Frequency Domain Simulations and Graphene Measurements
• Regular Bardeen AdS Black Hole as a Heat Engine
• From $s{l}_q(2)$ to a Parabosonic Hopf Algebra
• Strong Electron-Electron Interactions of a Tomonaga--Luttinger Liquid Observed in InAs Quantum Wires
• A Bochner Theorem for Dunkl Polynomials
• Through the eyes of a descriptor: Constructing complete, invertible descriptions of atomic environments
• Controlled Optofluidic Crystallization of Colloids Tethered at Interfaces
• Dunkl shift operators and Bannai-Ito polynomials
• Allostery and cooperativity in multimeric proteins: bond-to-bond propensities in ATCase
• On the Ambiguity of Interaction and Nonlinear Main Effects in a Regime of Dependent Covariates
• The algebra of dual -1 Hahn polynomials and the Clebsch-Gordan problem of sl_{-1}(2)
• A "Continuous" Limit of the Complementary Bannai-Ito Polynomials: Chihara Polynomials
• Analytical non-Hermitian description of Photonic Crystals with arbitrary Lateral and Transverse symmetry
• Topological spin liquids in the ruby lattice with anisotropic Kitaev interactions
• Lower-limb kinematics and kinetics during continuously varying human locomotion
• Possible odd-frequency Amperean magnon-mediated superconductivity in topological insulator -- ferromagnetic insulator bilayer
• "Solutocapillary Marangoni flow induced in waterbody by solute source"
• Orthogonal Polynomials in Mathematical Physics
• The ORNL Analysis Technique for Extracting $\beta$-Delayed Multi-Neutron Branching Ratios with BRIKEN
• Higher Order Quantum Superintegrability: a new "Painlevé conjecture"
• Non-perturbative analytical diagonalization of Hamiltonians with application to coupling suppression and enhancement in cQED
• The Heun-Racah and Heun-Bannai-Ito algebras
• Fluid-solid Floquet stability analysis of self-propelled heaving foils
• An infinite family of superintegrable Hamiltonians with reflection in the plane
• Hypergeometric Orthogonal Polynomials with respect to Newtonian Bases
• Charting the $q$-Askey scheme
• Jordan algebras and orthogonal polynomials
• Information bound for entropy production from the detailed fluctuation theorem
• Blind Image Denoising and Inpainting Using Robust Hadamard Autoencoders
• Transfer entropy computation using the Perron-Frobenius operator
• N-fold Supersymmetric Quantum Mechanics with Reflections
• An embedding of the Bannai-Ito algebra in $\mathcal{U}(\mathfrak{osp}(1,2))$ and $-1$ polynomials
• Prediction of $\mathrm{TiRhAs}$ as a Dirac Nodal Line Semimetal via First-Principles Calculations
• ClasSOMfier: A neural network for cluster analysis and detection of lattice defects
• Ni-P coatings electroplating - A review, Part I: Pure Ni-P alloy
• Abstract "hypergeometric" orthogonal polynomials
• On open quantum systems, effective Hamiltonians and device characterization
• Energy barriers between metastable states in first order quantum phase transitions
• varstan: An R package for Bayesian analysis of structured time series models with Stan
• Fairness and Missing Values
• Bivariate Bannai-Ito polynomials
• Antiferromagnet-mediated interlayer exchange: hybridization versus proximity effect
• Re-entrance of resistivity due to the interplay of superconductivity and magnetism in $\ce{Eu_{0.73}Ca_{0.27}(Fe_{0.87}Co_{0.13})2As2}$
• Free boson realization of the Dunkl intertwining operator in one dimension
• Approximation schemes for stochastic compliance-based topology optimization with many loading scenarios
• Experiential Learning Approach for Software Engineering Courses at Higher Education Level
• An Autonomous Programmable Actuator and Shape Reconfigurable Structures using Bistability and Shape Memory Polymers
• A superintegrable model with reflections on $S^3$ and the rank two Bannai-Ito algebra
• GOALS: Gradient-Only Approximations for Line Searches Towards Robust and Consistent Training of Deep Neural Networks
• Characterizing the impact of model error in hydrogeologic time series recovery inverse problems
• CMV matrices and little and big -1 Jacobi polynomials
• RSSI-based Outdoor Localization with Single Unmanned Aerial Vehicle
• Robust and stochastic compliance-based topology optimization with finitely many loading scenarios
• An Ab Initio Study of Aluminium self-compensation in Bulk Silicon
• Case study: Mapping potential informal settlements areas in Tegucigalpa with machine learning to plan ground survey
• Triggering flow asymmetry by lamella deflection during drop impact on superhydrophobic surfaces
• Experimental observation and computational modeling of radial Weibel instability in high intensity laser-plasma interactions
• Quantum process tomography of entangled photons as a probe of intermediates of singlet fission in a tetracene derivative
• Symmetric abstract hypergeometric polynomials
• A theoretical model for realistic local climates
• Diversity and its decomposition into variety, balance and disparity
• Laue three dimensional neutron diffraction
• Generating functions for the Bannai-Ito polynomials
• Dark Matter Effects on Stellar Populations in Globular Clusters
• Convolution identities for Dunkl orthogonal polynomials from the $\mathfrak{osp}(1|2)$ Lie superalgebra
• A Microscopic Explanation of Microwave Spin Pumping
• Jackson's $(-1)$-Bessel functions with the Askey-Wilson algebra setting
• Automated Movement Detection with Dirichlet Process Mixture Models and Electromyography