Generalization of Sheffer-<i>λ</i> polynomials

The aim of this study is to define a new generalization of Sheffer- lambda \lambda polynomials with the help of Sheffer polynomials and lambda \lambda -polynomials. For this family, explicit form, summation formulas, quasi-monomiality properties, differential equation and determinant representation are obtained. Subfamilies of these polynomials are introduced and similar properties for subfamilies are found. In addition, 3D graphs and the distribution of real roots are plotted for these subfamilies. Similarly, twice iterated Sheffer- lambda \lambda polynomials are defined and basic properties for this family and its subfamilies are obtained, and 3D graphs and the distribution of real roots are also investigated for the subfamilies.