On the multi variable hermite-based appell polynomials

The aim of this thesis is to investigate the Hermite-based Appell polynomials.In the first section, we define Appell polynomials and Hermite polynomials. In the second section, we introduce classical Bernoulli polynomials, classical Euler polynomials and Appell polynomials. After, some theorems which satisfy these polynomials are proven.In the final section, 2D-Bernoulli polynomials and Apostol-Bernoulli polynomials are given. Also some theorems are proved. Two relations are proved between Hermite-based Apostol-Bernoulli polynomials with Hurwitz-Lerch zeta function andbetween generalized Frobenius-Euler polynomaials with Hurwitz-Lerch zeta function.KEY WORDS: Bernoulli polynomials, Euler polynomials,Hermite polynomials, Appell polynomials,Appell sequences.