Hecke type operators and their applications

In this study, partial Hecke operators are de…ned. By using these operators,partial Hecke type operators are obtained. Many applications of these operators aregiven. The matrices corresponding to the partial Hecke operators are represented,which contain the Bernoulli and Euler polynomials. Some identities and relationsrelated to Genocchi type polynomials and generalized Euler type polynomials underthe partial Hecke operators and generalized partial Hecke operators, respectively.Also Hecke type operators Tp are applied to the special functions, which have anessential role in Mathematics.KEYWORDS : Generalized Bernoulli-Euler type polynomial,Generating functions, Hecke operators,Partial Hecke operators, Special functions