Discrete orthogonality relations for the multi-indexed orthogonal polynomials in discrete quantum mechanics with pure imaginary shifts
Abstract
The discrete orthogonality relations for the multi-indexed orthogonal polynomials in discrete quantum mechanics with pure imaginary shifts are investigated. We show that the discrete orthogonality relations hold for the case-(1) multi-indexed orthogonal polynomials of continuous Hahn, Wilson, and Askey-Wilson types, and we conjecture their normalization constants.
- Publication:
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Journal of Mathematical Physics
- Pub Date:
- May 2023
- DOI:
- arXiv:
- arXiv:2112.09358
- Bibcode:
- 2023JMP....64e3503O
- Keywords:
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- Mathematical Physics;
- High Energy Physics - Theory;
- Mathematics - Classical Analysis and ODEs;
- Nonlinear Sciences - Exactly Solvable and Integrable Systems
- E-Print:
- 32 pages. A reference and comments are added. To shorten the length, Section 4 and Appendix B are deleted. To appear in J.Math.Phys