Partial Hecke type operators and their applications

The aim of this paper is to not only give the matrix representation of partial Hecke type operators by means of the Bernoulli and Euler polynomials, but also functional equations and differential equations related to the partial Hecke type operators and special polynomials. By using these functional equations and differential equations, we derive some identities associated with special polynomials and the partial Hecke type operators. Moreover, we find many useful identities and relations using the partial Hecke operators. We also give some applications related to not only total and partial Hecke type operators, but also special polynomials and Euler identity for the Bernoulli numbers.