The Families of L-Series Associated with Decomposition of the Generating Functions


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ALKAN M., ŞİMŞEK Y.

FILOMAT, vol.30, no.7, pp.1789-1799, 2016 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 30 Issue: 7
  • Publication Date: 2016
  • Doi Number: 10.2298/fil1607789a
  • Journal Name: FILOMAT
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1789-1799
  • Keywords: q-Frobenius-Euler polynomials, q-series, Generating functions, Dirichlet L-function, Hurwitz zeta function, Riemann zeta function, Mellin transformation, ZETA, POLYNOMIALS, EULER, NUMBERS, EXTENSIONS, BERNOULLI
  • Akdeniz University Affiliated: Yes

Abstract

By using periodic functions from the nonnegative integers to the complex numbers, we generalize the generating function of the q-Apostol type Eulerian polynomials and numbers attached the character defined in [1]. Then using this generating function, we a construct new L-type series. By using periodic functions, we derive decomposition of the generating functions for the q-Euler numbers and polynomials. Applying the Mellin transformation to the decomposition of the generating functions, we introduce and investigate the various properties of a certain new family of the Dirichlet type L-series and the Dirichlet L-function. Finally, we derive many potentially useful results involving these functions polynomials and numbers.