Department of Mathematics
Permanent URI for this collection
Browse
Browsing Department of Mathematics by Author "Alwhishi, Sakina"
Now showing 1 - 1 of 1
Results Per Page
Sort Options
Item ON PROPERTIES OF HERMITE AND q−HERMITE I POLYNOMIALS AND THEIR LIMIT RELATIONS(2017-05-02) Alwhishi, Sakina; Sevinik Adıgüzel, Rezan; Turan, MehmetIn this thesis, some important properties of the Hermite polynomials and discrete q Hermite I polynomials are presented. Their properties will be considered in the same manner. The discrete q-Hermite I polynomials are the q-analogues of the Hermite polynomials. Such polynomials are an important class of the classical orthogonal polynomials and their q-analogues. The central idea in this thesis is to study the dif ferential and q-difference equation of hypergeometric type, three terms recurrence relations, Rodrigues formulas, orthogonalities and generating functions that the Her mite polynomials and its discrete version have. Hermite polynomials are obtained from the discrete q-Hermite I polynomials in the limiting case as q → 1. Such limit relation between the Hermite polynomials and the discrete q-Hermite I polynomials on each properties that is introduced in the thesis are considered in detailed.