Families of polynomial with stirling coefficient

In this thesis, a new family of polynomial with Stirling coefficients is defined. It is determined that family of polynomials is reduced to Bernoulli and Euler numbers and some generalizations of these numbers, which have an important place in number theory, along with geometric polynomials and higher order geometric polynomials. To obtain the properties of this new polynomial, its generating function is calculated in terms of hypergeometric functions. The properties of polynomial family are investigated by using some properties provided by the hypergeometric functions. In particular cases, new and known relations for the aformentioned number and polynomial families are reached.