A generating function and formulae defining the first-associated Meixner-Pollaczek polynomials

While considering nonlinear coherent states with anti- holomorphic coefficients we identify as first- associated Meixner- Pollaczek polynomials the orthogonal polynomials arising from shift operators which are defined by the sequence x(n) = (n + 1)(2). We give a formula defining these polynomials by writing down their generating function. This also leads to construct a Bargmann- type integral transform whose kernel is given in terms of a Psi(1) Humbert's confluent hypergeometric function.