Harmonic geometric polynomials and numbers

In this thesis, we first obtain the generating function of the harmonic-geometric polynomials. Using the generating function, new closed-form expressions for harmonic geometric and geometric polynomials are derived. Furthermore, we investigate whether the sums of products of two geometric polynomials can be expressed in terms of harmonic-geometric and geometric polynomials, and it is shown that such expressions are indeed possible. Finally, we establish the relationships between harmonic geometric polynomials and the Euler and Bernoulli numbers. Through these connections, the properties obtained for the polynomials are extended to these special numbers.