A STUDY OF GAUSS' HYPERGEOMETRIC POLYNOMIALS AND THEIR APPLICATIONS

Abstract

ABSTRACT : In this thesis, we present a systematic study of Gauss' hypergeometric polynomials and their applications. We define the Gauss' hypergeometric polynomials by means of a generating function, a differential equation and an integral representation. Some integrals, orthogonal properties, semi-orthogonal properties and orthogonal symmetries of Gauss' hypergeometric polynomials and their particular cases are also presented. Some integrals and expansion formulae for Fox's H-function involving Gauss' hypergeometric polynomials are also given. We formulate and solve some partial differential equations related to the problems of heat conduction and other applied sciences, solutions of which lead to the Jacobi polynomials and the Legendre functions.