The Exceptional (X_{\ell}) (q)-Racah Polynomials

Abstract

The exceptional Racah and q-Racah polynomials are constructed. Together with the exceptional Laguerre, Jacobi, Wilson and Askey-Wilson polynomials discovered by the present authors in 2009, they exhaust the generic exceptional orthogonal polynomials of a single variable.

25 pages

References in corpus (1)

• Exactly solvable `discrete' quantum mechanics; shape invariance, Heisenberg solutions, annihilation-creation operators and coherent states

Cited by in corpus (28)

• Exactly Solvable Quantum Mechanics and Infinite Families of Multi-indexed Orthogonal Polynomials
• Discrete Quantum Mechanics
• Multi-indexed (q-)Racah Polynomials
• Extensions of solvable potentials with finitely many discrete eigenstates
• Orthogonal Polynomials from Hermitian Matrices II
• Recurrence Relations of the Multi-Indexed Orthogonal Polynomials
• Dual Christoffel transformations
• Prepotential approach to solvable rational extensions of Harmonic Oscillator and Morse potentials
• Recurrence Relations of the Multi-Indexed Orthogonal Polynomials : III
• DARBOUX partners of pseudoscalar Dirac potentials associated with exceptional orthogonal polynomials
• Equivalences of the Multi-Indexed Orthogonal Polynomials
• Recurrence Relations of the Multi-Indexed Orthogonal Polynomials : II
• Exceptional orthogonal polynomials and new exactly solvable potentials in quantum mechanics
• Recurrence Relations of the Multi-Indexed Orthogonal Polynomials IV : closure relations and creation/annihilation operators
• Solutions to the Painlevé V equation through supersymmetric quantum mechanics
• Exactly Solvable Discrete Quantum Mechanical Systems and Multi-indexed Orthogonal Polynomials of the Continuous Hahn and Meixner-Pollaczek Types
• Generalized Rayleigh and Jacobi processes and exceptional orthogonal polynomials
• Exactly solvable discrete time Birth and Death processes
• Quasi-Hermitian Hamiltonians associated with exceptional orthogonal polynomials
• New Determinant Expressions of the Multi-indexed Orthogonal Polynomials in Discrete Quantum Mechanics
• Type II Multi-indexed Little $q$-Jacobi and Little $q$-Laguerre Polynomials
• Recurrence Relations of the Multi-Indexed Orthogonal Polynomials V : Racah and $q$-Racah types
• Dual Polynomials of the Multi-Indexed ($q$-)Racah Orthogonal Polynomials
• New Finite Type Multi-Indexed Orthogonal Polynomials Obtained From State-Adding Darboux Transformations
• Quantum vs Classical Birth and Death Processes; Exactly Solvable Examples
• Casoratian Identities for the Discrete Orthogonal Polynomials in Discrete Quantum Mechanics with Real Shifts
• Multi-indexed Orthogonal Polynomials of a Discrete Variable and Exactly Solvable Birth and Death Processes
• Recurrence Relations of the Multi-Indexed Orthogonal Polynomials VI : Meixner-Pollaczek and continuous Hahn types