On knot polynomials of twist knot

This study consists of four chapters. In the first chapter, it is given the introduction part. In the second chapter, some basic concepts for knots are introduced. In the third chapter, basic information about oriented and unoriented knot polynomials and some of their properties are discussed. In the fourth chapter, which is the original part of this study, the formulas for HOMFLY polynomials of oriented twist knots and Kauffman L and F polynomials of unoriented twist knots are obtained, and the mentioned knot polynomials for twist knots are defined as fourth-order recurrence relations. Here, the previous formulas and relations related to the knot polynomials of (2,n)-torus links are used to obtain some results. In addition, some recursive properties of the relations found are examined and their generating functions, general solutions and explicit forms are given.