Divided-difference equation, inversion, connection, multiplication and linearization formulae of the continuous Hahn and the Meixner–Pollaczek polynomials

From the study of various properties of some difference operators, we prove in the first part of this work that the continuous Hahn and the Meixner–Pollaczek polynomials are solutions of a second-order divided-difference equation of hypergeometric- type. Next, using some algorithmic tools, we solve the inversion, connection, multiplication and linearization problems for the continuous Hahn and the Meixner–Pollaczek polynomials.