On Generating Functions for the Special Polynomials

ŞİMŞEK Y.

FILOMAT, vol.31, no.1, pp.9-16, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 31 Issue: 1
  • Publication Date: 2017
  • Doi Number: 10.2298/fil1701009s
  • Journal Name: FILOMAT
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.9-16
  • Keywords: Euler numbers, Euler polynomials, Frobenius-Euler numbers, Frobenius-Euler polynomials, Apostol-Bernoulli polynomials, Apostol-Bernoulli numbers, Generating functions, APOSTOL-BERNOULLI, Q-EXTENSIONS, EULER, NUMBERS
  • Akdeniz University Affiliated: Yes

Abstract

The aim of this paper is to investigate and give a new family of Apell type polynomials, which are related to the Euler, Frobenius-Euler and Apostol-Bernoulli polynomials and numbers and also the generalized Stirling numbers of the second kind etc. The results presented in this paper are based upon the theory of the generating functions. By using functional equations of these generating functions, we drive some identities and relations for these numbers and polynomials. Moreover, we give a computation algorithm these numbers.