Boole and q-Boole polynomials

This thesis consist of four chapters. In first chapter, we give definitions and theorems which compose a basic for next chapters. In second chapter, Boole numbers and polynomials are defined and given their main properties. Also, relations are investigated between Boole numbers and polynomials and first Stirling numbers, second Stirling numbers, Euler numbers and polynomials which are important in Analytic Number Theory. In third chapter, q-Boole numbers and polynomials are defined and given their basic properties. In last section of thesis,fourth chapter, new identities are obtained between Boole numbers and polynomials and some special numbers and polynomials which are called mixed-type polynomials.