Higher-order Euler-type polynomials and their applications

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Aygunes A. A.

FIXED POINT THEORY AND APPLICATIONS, vol.2013, 2013 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 2013
  • Publication Date: 2013
  • Doi Number: 10.1186/1687-1812-2013-40
  • Journal Name: FIXED POINT THEORY AND APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: generalized partial Hecke operators, higher-order Euler-type polynomials, higher-order Euler-type numbers, Apostol-Bernoulli polynomials, Frobenius-Euler polynomials, Euler polynomials, Euler numbers, functional equation, generating functions, GENERATING-FUNCTIONS, BERNOULLI, NUMBERS, ZETA, IDENTITIES, ANALOGS, SERIES
  • Akdeniz University Affiliated: No

Abstract

In this paper, we construct generating functions for higher-order Euler-type polynomials and numbers. By using the generating functions, we obtain functional equations related to a 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.