On some problems of hypergeometric Polynomials

Abstract

The present thesis entitled On some problems of hypergeometric polynomials is an outcome of the studies made by the author at the Department of Applied Mathematics, Aligarh Muslim University, Aligarh. The thesis consists of eight chapters. Articles, definitions and equations have been numbered chapter wise in such a way that, when read as decimals they stand in their proper order e.g., (6.5.1) refers to equation number 1 of section 5 of chapter 6. A brief review of some important special functions, some integral transforms, the definitions, notations and miscellaneous results which commonly arise in practice and explore many of their salient properties, are given in the first chapter. Chapter II introduces modified Hermite polynomials of one and two variables, The aim of the present chapter is to investigate these two polynomials and acquire some important results such as generating functions, recurrence relations, Rodrigues formula, orthogonality conditions, expansion formulae, integrals, fractional integrals, fractional derivatives, operator representations and other properties of the above polynomials.