Abstract
This paper gives a solution, without the use of the three-term recurrence relation, of the problem posed in Ismail (Classical and Quantum Orthogonal Polynomials in One Variable, Cambridge University Press, Cambridge, 2005) (Problem 24.8.2, p. 658): that the hypergeometric representation of the general Pollaczek polynomials is a polynomial in cos(theta) of degree n. Chu solved in (Ramanujan J. 13(1-3): 221-225, 2007) the problem in a particular case. We use elementary properties of functions of complex variables and Pfaff's transformation on hypergeometric (2) F (1)-series.