Higher order Euler type polynomials and their applications

In this paper, we construct generating functions for higher order Euler type polynomials and numbers. By using the generating functions, we obtain the functional equations related to generalized partial Hecke operator and Euler type polynomials and numbers. A special case of higher order Euler type polynomials is eigenfunctions for the generalized partial Hecke operators. Moreover, we give not only some properties but also applications for these polynomials and numbers.