Partial Hecke-type operators and their applications

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Aygunes A. A., ŞİMŞEK Y.

BOUNDARY VALUE PROBLEMS, vol.2013, 2013 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 2013
  • Publication Date: 2013
  • Doi Number: 10.1186/1687-2770-2013-46
  • Journal Name: BOUNDARY VALUE PROBLEMS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: Bernoulli polynomial, Euler polynomial, partial Hecke-type operator, total Hecke-type operator, Hurwitz zeta function, partial zeta function, BERNOULLI, NUMBERS, EULER, ZETA
  • Akdeniz University Affiliated: Yes

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.