Some families of hypergeometric polynomials and associated multiple integral representations

Abstract

The main object of this paper is to investigate several general families of hypergeometric polynomials and their associated multiple integral representations. 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.

Keywords:

• hypergeometric polynomials
• integral representations
• Gamma function
• Eulerian beta integral
• generalized Rice polynomials
• generating functions
• Srivastava polynomials
• Lagrange polynomials
• Lagrange–Hermite polynomials
• Pochhammer symbol
• Hermite–Kampé de Fériet polynomials

2010 Mathematics Subject Classifications :

• Primary 33C45
• 33C65
• Secondary 42C05

Acknowledgements

The present investigation was supported, in part, by the National Science Council of the Republic of China under Grant NSC 99-2811-M-033-014 and, in part, by the National Science Council of the Republic of China under Grant NSC 99-2115-M-033-002.