A generalization of Gottlieb polynomials in several variables

Gottlieb polynomials were introduced and investigated in 1938, and then have been cited in several articles. Very recently, Khan and Akhlaq introduced and investigated Gottlieb polynomials in two and three variables to give their generating functions. Subsequently, Khan and Asif investigated the generating functions for the q-analogue of Gottlieb polynomials. In this sequel, by modifying Khan and Akhlaq's method, we show how to generalize the Gottlieb polynomials in m variables to present two generating functions of the generalized Gottlieb polynomials phi(m)(n)(.). Furthermore, it should be noted that, since one of the two generating functions is expressed in terms of the well-developed Lauricella series F(D)((m)) [.], certain interesting and (potentially) useful identities for phi(m)(n)(.) and its reducible cases are shown to be easily found. (C) 2011 Elsevier Ltd. All rights reserved.