Recurrence relations of the multi-indexed orthogonal polynomials V: Racah and q -Racah types
Copyright policy )Recurrence relations of the multi-indexed orthogonal polynomials V: Racah and q -Racah types
In previous papers, we discussed the recurrence relations of the multi-indexed orthogonal polynomials of the Laguerre, Jacobi, Wilson, and Askey-Wilson types. In this paper, we explore those of the Racah and q-Racah types. For the M-indexed (q-)Racah polynomials, we derive 3 + 2M term recurrence relations with variable dependent coefficients and 1 + 2L term (L ≥ M + 1) recurrence relations with constant coefficients. Based on the latter, the generalized closure relations and the creation and annihilation operators of the quantum mechanical systems described by the multi-indexed (q-)Racah polynomials are obtained. In Appendix B and Appendix C, we present a proof and some data of the recurrence relations with constant coefficients for the multi-indexed Wilson and Askey-Wilson polynomials.
- Shinshu University Japan
- Shinshu University Japan
- Shinshu University Japan
- Shinshu University Japan
Operator algebra methods applied to problems in quantum theory, High Energy Physics - Theory, Nonlinear Sciences - Exactly Solvable and Integrable Systems, FOS: Physical sciences, Mathematical Physics (math-ph), multi-indexed orthogonal polynomials of the \(q\)-Racah type, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), High Energy Physics - Theory (hep-th), Mathematics - Classical Analysis and ODEs, Many-body theory; quantum Hall effect, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Numerical aspects of recurrence relations, Exactly Solvable and Integrable Systems (nlin.SI), Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, Mathematical Physics
Operator algebra methods applied to problems in quantum theory, High Energy Physics - Theory, Nonlinear Sciences - Exactly Solvable and Integrable Systems, FOS: Physical sciences, Mathematical Physics (math-ph), multi-indexed orthogonal polynomials of the \(q\)-Racah type, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), High Energy Physics - Theory (hep-th), Mathematics - Classical Analysis and ODEs, Many-body theory; quantum Hall effect, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Numerical aspects of recurrence relations, Exactly Solvable and Integrable Systems (nlin.SI), Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, Mathematical Physics
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