Dejenerate type2 poly-Bernoulli polynomials with a q-parameter including the Gould-Hopper polynomials

This thesis consists of eight chapters. The first chapter is introduction part which includes the motivation of this thesis and some fundamental definitions and formulas. The familiar Bernoulli polynomials in the second chapter, the poly-Bernoulli polynomials in the third chapter, the degenerate Bernoulli polynomials in the forth chapter, the Bernoulli polynomials with a q parameter in the fifth chapter, the Gould-Hopper based Bernoulli polynomials in conjuction with their some extensions in the sixth chapter are examined extensively. The seventh chapter deals with the Gould-Hopper based fully degenerate type2 poly-Bernoulli polynomials with a q parameter associated with the polyexponential function and degenerate exponential function and investigate some of their properties, relations and formulas including addition formulas, difference rule properties, recurrence relations, implicit summation formulas, symmetric formulas.