We consider the generalized Meixner-Pollaczek (GMP) polynomials of a variable and parameters , , , defined via the generating function
We find the three-term recurrence relation, the explicité formula, the hypergeometric representation, the difference equation and the orthogonality relation for GMP polynomials . Moreover, we study the special case of corresponding to the choice and , which leads to some interesting families of polynomials. The limiting case ( ) of the sequences of polynomials is obtained, and the orthogonality relation in the strip is shown.
MSC: 33C45, 30C10, 30C45, 39A60.