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Quantum Foundations Open Quantum Systems Decoherence Entanglement Theory Quantum Correlations Quantum Simulation

Casoratian Identities for the Wilson and Askey-Wilson Polynomials

arXiv
Authors: Satoru Odake, Ryu Sasaki

Year

2013

Paper ID

33151

Status

Preprint

Abstract Read

~2 min

Abstract Words

83

Citations

N/A

Abstract

Infinitely many Casoratian identities are derived for the Wilson and Askey-Wilson polynomials in parallel to the Wronskian identities for the Hermite, Laguerre and Jacobi polynomials, which were reported recently by the present authors. These identities form the basis of the equivalence between eigenstate adding and deleting Darboux transformations for solvable (discrete) quantum mechanical systems. Similar identities hold for various reduced form polynomials of the Wilson and Askey-Wilson polynomials, e.g. the continuous q-Jacobi, continuous (dual) (q-)Hahn, Meixner-Pollaczek, Al-Salam-Chihara, continuous (big) q-Hermite, etc.

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  • Infinitely many Casoratian identities are derived for the Wilson and Askey-Wilson polynomials in parallel to the Wronskian identities for the Hermite, Laguerre and Jacobi...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1308.4240 [2] arXiv https://arxiv.org/abs/1308.4240 [3] Publisher https://arxiv.org/abs/1308.4240

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