Certain results on generating functions related to the associated Meixner-Pollaczek polynomials

In the present paper we first derive a new form of a generating function for the c-associated Meixner-Pollaczek polynomials. This generating function is of particular importance since its several reducible cases yield special cases of interest which also include an elegant extension of the main generating function of Ahbli and Mouayn [Integral Transform Spec Funct. 2018;28:352-366] that stems from an application of nonlinear coherent states with anti-holomorphic coefficients in applied physics. We further establish a new generating function for the associated Meixner polynomials and obtain a bilinear series relation which transforms a series involving the product of the c-associated Meixner-Pollaczek polynomials and Meixner-Pollaczek polynomials in terms of a series involving Lagrange polynomials. Several corollaries and special cases of the main results are also mentioned.