Orthogonality of the Meixner-Pollaczek polynomials beyond Favard's theorem

We extend the family of Meixner-Pollaczek polynomials {P-n((lambda))(.;phi)}(n = 0)(infinity), classically defined for lambda > 0 and 0 < phi < pi, to arbitrary complex values of the parameter lambda, in such a way that both polynomial systems (the classical and the new generalized ones) share the same three term recurrence relation. The values lambda(N) = (1 - N)/2, with N a positive integer, are the only ones for which no orthogonality condition can be deduced from Favard's theorem. In this paper we introduce a non-standard discrete-continuous inner product with respect to which the generalized Meixner-Pollaczek polynomials {P-n((lambda N))(.;phi)}(n = 0)(infinity) become orthogonal.