2022-08-15T12:21:12Zhttps://soar-ir.repo.nii.ac.jp/oaioai:soar-ir.repo.nii.ac.jp:000117152021-09-02T05:45:52Z1169:1170Equivalences of the multi-indexed orthogonal polynomialsOdake, SatoruMulti-indexed orthogonal polynomials describe eigenfunctions of exactly solvable shape-invariant quantum mechanical systems in one dimension obtained by the method of virtual states deletion. Multi-indexed orthogonal polynomials are labeled by a set of degrees of polynomial parts of virtual state wavefunctions. For multi-indexed orthogonal polynomials of Laguerre, Jacobi, Wilson, and Askey-Wilson types, two different index sets may give equivalent multi-indexed orthogonal polynomials. We clarify these equivalences. Multi-indexed orthogonal polynomials with both type I and II indices are proportional to those of type I indices only (or type II indices only) with shifted parameters.ArticleJOURNAL OF MATHEMATICAL PHYSICS. 55(1):013502 (2014)journal articleAMER INST PHYSICS2014-01application/pdfJOURNAL OF MATHEMATICAL PHYSICS155135020022-2488AA00701758https://soar-ir.repo.nii.ac.jp/record/11715/files/Equivalences_multi-indexed_orthogonal_polynomials.pdfeng10.1063/1.4859795https://doi.org/10.1063/1.4859795CopyrightÂ© 2014 AIP Publishing LLC.