Some families of hypergeometric polynomials and associated integral representations (Q596769)

In this paper the authors consider four families of polynomials, which are special or limiting cases of polynomials of the form \[ S_{n}^{N}(z):=\sum_{k=0}^{[n/N]}\frac{(-n)_{Nk}}{k!}\,A_{n,\,k}\,z^{k}, \] where \(A_{n,\,m}\) is a suitably bounded double sequence of real or complex numbers. They derive some single-, double-, and triple-integral representations associated with these families of polynomials. They also consider several known or new special cases and consequences of their main results, involving classical orthogonal polynomials and various other related hypergeometric polynomials. Concluding their investigation, the authors remark that each of the integral representation obtained in this paper, may be viewed as a linearization relationship for the product of two different members of the associated family of hypergeometric polynomials.