Report
Casoratian Identities for the Discrete Orthogonal Polynomials in Discrete Quantum Mechanics with Real Shifts
| العنوان: | Casoratian Identities for the Discrete Orthogonal Polynomials in Discrete Quantum Mechanics with Real Shifts |
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| المؤلفون: | Odake, Satoru |
| المصدر: | Prog. Theor. Exp. Phys. 2017 (2017) 123A02 (30pp) |
| سنة النشر: | 2017 |
| المجموعة: | Mathematics Mathematical Physics Nonlinear Sciences |
| مصطلحات موضوعية: | Mathematical Physics, Mathematics - Classical Analysis and ODEs, Nonlinear Sciences - Exactly Solvable and Integrable Systems |
| الوصف: | In our previous papers, the Wronskian identities for the Hermite, Laguerre and Jacobi polynomials and the Casoratian identities for the Askey-Wilson polynomial and its reduced form polynomials were presented. These identities are naturally derived through quantum mechanical formulation of the classical orthogonal polynomials; ordinary quantum mechanics for the former and discrete quantum mechanics with pure imaginary shifts for the latter. In this paper we present the corresponding identities for the discrete quantum mechanics with real shifts. Infinitely many Casoratian identities for the $q$-Racah polynomial and its reduced form polynomials are obtained. Comment: 37 pages. Comments, a reference and proportionality constants for q-Racah case are added. Sec.3.3 is moved to App.B. To appear in PTEP |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1093/ptep/ptx165 |
| URL الوصول: | http://arxiv.org/abs/1708.01830 |
| رقم الانضمام: | edsarx.1708.01830 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1093/ptep/ptx165 |
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