A NEW FAMILY OF FUBINI TYPE NUMBERS AND POLYNOMIALS ASSOCIATED WITH APOSTOL-BERNOULLI NUMBERS AND POLYNOMIALS

KILAR N., ŞİMŞEK Y.

JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, vol.54, no.5, pp.1605-1621, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 54 Issue: 5
  • Publication Date: 2017
  • Doi Number: 10.4134/jkms.j160597
  • Journal Name: JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1605-1621
  • Keywords: Bernoulli numbers, Apostol-Bernoulli numbers, ApostolBernoulli polynomials, Frobenius-Euler numbers, Stirling numbers, Fubini numbers, generating functions, functional equations, binomial coefficients, combinatorial sum, UNIFIED PRESENTATION, EULER, UNIFICATION, IDENTITIES, ZETA
  • Akdeniz University Affiliated: Yes

Abstract

The purpose of this paper is to construct a new family of the special numbers which are related to the Fubini type numbers and the other well-known special numbers such as the Apostol-Bernoulli numbers, the Frobenius-Euler numbers and the Stirling numbers. We investigate some fundamental properties of these numbers and polynomials. By using generating functions and their functional equations, we derive various formulas and relations related to these numbers and polynomials. In order to compute the values of these numbers and polynomials, we give their recurrence relations. We give combinatorial sums including the Fubini type numbers and the others. Moreover, we give remarks and observation on these numbers and polynomials.