Recurrence relations of the multi-indexed orthogonal polynomials. VI. Meixner–Pollaczek and continuous Hahn types

DOI10.1063/1.5144338zbMATH Open1443.33023arXiv1912.12381OpenAlexW3100307037MaRDI QIDQ3298961

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Publication date: 16 July 2020

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Abstract: In previous papers, we discussed the recurrence relations of the multi-indexed orthogonal polynomials of the Laguerre, Jacobi, Wilson, Askey-Wilson, Racah and $q$-Racah types. In this paper we explore those of the Meixner-Pollaczek and continuous Hahn types. For the $M$-indexed Meixner-Pollaczek and continuous Hahn polynomials, we present $3+2M$ term recurrence relations with variable dependent coefficients and $1+2L$ term ($LgeqM+1$) recurrence relations with constant coefficients. Based on the latter, the generalized closure relations and the creation/annihilation operators of the quantum mechanical systems described by the multi-indexed Meixner-Pollaczek and continuous Hahn polynomials are obtained.

Full work available at URL: https://arxiv.org/abs/1912.12381

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