Genocchi and q-genocchi polynomials

This thesis is formed from four sections. In the first section, it is investigated under three main headings including important definitions and theorems, q-analysis and p-adic analysis. In the second section, Genocchi numbers and polynomials, Genocchi polynomials of higher order are stated and investigated their important properties. In the third section, q-Genocchi numbers and polynomials, which generalizes the classical Genocchi numbers and polynomials, are shown. In the last section of this thesis, weighted q-Genocchi numbers and polynomials are defined and given their analytic continuation.