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

Recurrence Relations of the Multi-Indexed Orthogonal Polynomials VI : Meixner-Pollaczek and continuous Hahn types