Multivariable generalized sylvester polynomials

This thesis consists of four chapters. The first section is devoted to the introduction. A brief introduction to what this thesis is about and the literature summary of Sylvester polynomials are given. In the second part, some definitions and lemmas are given. In the third chapter, univariate Sylvester polynomial, generalized Sylvester polynomials and modified generalized Sylvester polynomials are composed of properties. In the fourth chapter, Sylvester polynomials with multiple variables are introduced and their properties are given. In addition, theorems for these polynomials yielding bilinear and bilateral generating functions were obtained. The results and applications of the theorems given here were examined. Correlations between Appell and generalized Lauricella functions of multivariable Sylvester polynomials were examined. Exceptions were given. In the last chapter, some conclusions and recommendations are presented for this thesis.