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Open Access Research

Partial Hecke-type operators and their applications

Aykut Ahmet Aygunes and Yilmaz Simsek*

Author affiliations

Department of Mathematics, Faculty of Science, Akdeniz University, Campus, Antalya, 07058, Turkey

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Citation and License

Boundary Value Problems 2013, 2013:46  doi:10.1186/1687-2770-2013-46

Published: 6 March 2013

Abstract

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

MSC: 05B20, 11B68, 11F25.

Keywords:
Bernoulli polynomial; Euler polynomial; partial Hecke-type operator; total Hecke-type operator; Hurwitz zeta function; partial zeta function