Multi-indexed Jacobi polynomials and Maya diagrams

Abstract

Multi-indexed Jacobi polynomials are defined by the Wronskian of four types of eigenfunctions of a deformed Pöschl-Teller Hamiltonian. We give a correspondence between multi-indexed Jacobi polynomials and pairs of Maya diagrams, and we show that any multi-indexed Jacobi polynomial is essentially equal to some multi-indexed Jacobi polynomial of two types of eigenfunction. As an application, we show a Wronskian-type formula of some special eigenstates of the deformed Pöschl-Teller Hamiltonian.

12 pages

References in corpus (5)

• Infinitely many shape invariant potentials and new orthogonal polynomials
• Exceptional orthogonal polynomials, exactly solvable potentials and supersymmetry
• Extended Krein-Adler theorem for the translationally shape invariant potentials
• Equivalences of the Multi-Indexed Orthogonal Polynomials
• Global Solutions of Certain Second-Order Differential Equations with a High Degree of Apparent Singularity

Cited by in corpus (10)

• Exceptional Jacobi polynomials
• Exceptional Laguerre polynomials
• Recurrence Relations of the Multi-Indexed Orthogonal Polynomials : III
• A Bochner type classification theorem for exceptional orthogonal polynomials
• Shape invariance and equivalence relations for pseudowronskians of Laguerre and Jacobi polynomials
• Equivalences of the Multi-Indexed Orthogonal Polynomials
• Recurrence Relations of the Multi-Indexed Orthogonal Polynomials IV : closure relations and creation/annihilation operators
• Exactly Solvable Discrete Quantum Mechanical Systems and Multi-indexed Orthogonal Polynomials of the Continuous Hahn and Meixner-Pollaczek Types
• New Determinant Expressions of the Multi-indexed Orthogonal Polynomials in Discrete Quantum Mechanics
• Exactly Solvable Quantum Mechanics