Harmonic exponential polynomials and numbers

In this thesis, the generating function of harmonic exponential polynomials is obtained by means of generating functions of harmonic numbers and hypergeometric functions. Using this generating function, new relations obtained between the Bernoulli numbers (which has an important place in number theory) and harmonic exponential polynomials. Within this context, with the help of the derivative of the obtained generating function, new connections have been found between harmonic exponential polynomials, exponential polynomials and the derivatives of these polynomials. Additionally, a recursive relation between harmonic exponential polynomials and Bernoulli numbers is established, along with an integral representation in terms of the exponential polynomials.