We study a class of polynomials ${f^{c,r}_{n,m}(x)}$, where $c$ is some real number, $r\in$ $\mathbb{N}$ $\cup{0}$, $m \in$ $\mathbb{N}$. These polynomials are defined by the generating function. Also, for these polynomials we find an explicit representation in the form of the hypergeometric function; some identities of the convolution type are presented; some special cases are shown. The special cases of these polynomials are: Panda's polynomials [2], [4]; the generalized Laguerre polynomials [1], [6]; the Celine Fasenmyer polynomials [3].