Generating function for q-Eulerian polynomials and their decomposition and applications

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ALKAN M., ŞİMŞEK Y.

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

  • Publication Type: Article / Article
  • Volume: 2013
  • Publication Date: 2013
  • Doi Number: 10.1186/1687-1812-2013-72
  • Journal Name: FIXED POINT THEORY AND APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: Euler numbers, Frobenius-Euler numbers, Frobenius-Euler polynomials, q-Frobenius-Euler polynomials, q-series, generating function, character chi of the finite abelian groups G, APOSTOL-BERNOULLI, Q-EXTENSIONS, Q-ANALOG, NUMBERS, SERIES, ORDER
  • Open Archive Collection: AVESIS Open Access Collection
  • Akdeniz University Affiliated: Yes

Abstract

The aim of this paper is to define a generating function for q-Eulerian polynomials and numbers attached to any character chi of the finite cyclic group G. We derive many functional equations, q-difference equations and partial deferential equations related to these generating functions. By using these equations, we find many properties of q-Eulerian polynomials and numbers. Using the generating element of the finite cyclic group G and the generating element of the subgroups of G, we show that the generating function with a conductor f can be written as a sum of the generating function with conductors which are less than f.