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

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 (L ≥ M + 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.