Generating functions of hermite type milne-thomson polynomials and their applications in computational sciences

In this thesis, Hermite type Milne-Thomson polynomials and their generating functions have been studied. By using these generating functions constructed with the help of the Euler's formula and trigonometric functions, some families of r-parametric Hermite-based Milne-Thomson type polynomials have also been studied. The definitions and some properties of some well-known families of special numbers and polynomials, such as families of Bernoulli type numbers and polynomials, families of Euler type numbers and polynomials, families of Genocchi type numbers and polynomials, and the Stirling numbers, have been given. With the help of the newly obtained generating functions and their functional equations, special integral formulas and trigonometric functions, we have been given formulas, relations and identities including the r-parametric Hermite-based Milne-Thomson polynomials, the r-parametric Hermite type polynomials and some other families of special polynomials. In addition, relationships and combinatorial sums for some families of special numbers and polynomials, which include especially the Apostol-Bernoulli numbers of higher order, the Apostol-Euler numbers of higher order, the Apostol-Genocchi numbers of higher order, the tangent numbers, the cotangent numbers, the Chebyshev polynomials, the Dickson polynomials, Fubini type numbers and polynomials, the generalized Hermite-Kampè de polynomials, Milne-Thomson type polynomials, and two parametric kinds of Apostol type polynomials, have been obtained. In this thesis, some special cases of generating functions, including families of the r-parametric Hermite-based Milne-Thomson type polynomials, have also been presented in tables. Additionally, for some families of special numbers and polynomials, computational algorithms have been given and by coding some of these algorithms in the Mathematica package program with the help of the Wolfram programming language, the values for families of the r-parametric Hermite type polynomials and families of the r-parametric Hermite-based Milne-Thomson polynomials have been calculated, and their graphs and surfaces have been drawn.