The main object of this paper is to investigate several general families of hypergeometric polynomials and their associated multiple integral representations. By suitably specializing our main results, the corresponding integral representations are deduced for such familiar classes of hypergeometric polynomials as (for example) the generalized Bedient polynomials of the first and second kinds. Each of the integral representations, which are derived in this paper, may be viewed also as a linearization relationship for the product of two different members of the associated family of hypergeometric polynomials.
The incomplete Gamma function γ(α, x) and its associated functions γ(α, x+) and γ(α, x−) are defined as locally summable functions on the real line and some convolutions and neutrix convolutions of these functions and the functions x r and x r − are then found.