In 1972, H. M. Srivastava introduced and investigated the general polynomial family \[ S_{n}^{N}(z)=\sum_{k=0}^{[n/N]} {{(-n)_{Nk}}\over {k!}}A_{n,k}z^{k}, \] where \(n\in {\mathbb N}_{0}\), \(N\in {\mathbb N}\), \([k]\) is the greatest integer less or equal to \(k\in \mathbb{R}\), \((\lambda)_{\nu}\) is the Pochhammer symbol and \(A_{n,k}\) is a suitably bounded double sequence of parameters.
In this paper, the authors find multiple integral representations of polynomials which belong to the family \(S_{n}^{N}(z)\). Each of these polynomials can be rewritten as a generalized hypergeometric polynomial, so the obtained integral representations can also be rewritten as the product of two members of the associated family of hypergeometric polynomials. The obtained general results can be applied to some familiar simpler classes of hypergeometric polynomials, such as Lagrange polynomials, Shively’s pseudo-Laguerre polynomials and generalized Bessel polynomials.