Relations between Leibnitz type numbers and some special sums

In this thesis, the relations among the Leibnitz numbers and Leibnitz type numbers and some of their special sums are studied. With the help of generating functions and their functional equations, some properties of Leibnitz type numbers and polynomials are given. Similarly, relations among the Bernstein polynomials, the Stirling numbers, the Catalan numbers, the Bernoulli numbers and polynomials, the Euler numbers and polynomials, the Genocchi numbers and polynomials are investigated using generating functions techniques. In addition, with the aid of generating functions, the Leibnitz type numbers and polynomials and some special sums, relations and formulas are given. The results obtained in this thesis may be used both in mathematics and in other branches of science.