In this paper, we give some relations between multivariable Laguerre polynomials and other well-known multivariable polynomials. We get various families of multilinear and multilateral generating functions for these polynomials. Some special cases are also presented.

Since Gottlieb introduced and investigated the so-called Gottlieb polynomials in 1938, which are discrete orthogonal polynomials, many researchers have investigated these polynomials from diverse angles. In this paper, we aimed to investigate the q-extensions of these polynomials to provide certain q-generating functions for three sequences associated with a finite power series whose coefficients are products of the known q-extended multivariable and multiparameter Gottlieb polynomials and another non-vanishing multivariable function. Furthermore, numerous possible particular cases of our main identities are considered. Finally, we return to Khan and Asif’s q-Gottlieb polynomials to highlight certain connections with several other known q-polynomials, and provide its q-integral representation. Furthermore, we conclude this paper by disclosing our future investigation plan.

Cesàro polynomials have been extended in various ways and applied in diverse areas. In this paper, we aim to introduce a multivariable and multiparameter generalization of Cesàro polynomials. Then we explore several generating functions, an addition formula, a differential-recurrence relation, a multiple integral formula for this extended Cesàro polynomial, as well as a multiple integral formula whose kernel is this extended Cesàro polynomial. Also we present several bilinear and bilateral generating functions for this extended Ces`aro polynomial, two of whose examples are demonstrated.