Families of unified and modified presentation of Fubini numbers and polynomials

Kilar N., ŞİMŞEK Y.

Montes Taurus Journal of Pure and Applied Mathematics, cilt.5, sa.1, ss.1-21, 2023 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 5 Sayı: 1
  • Basım Tarihi: 2023
  • Dergi Adı: Montes Taurus Journal of Pure and Applied Mathematics
  • Derginin Tarandığı İndeksler: Scopus
  • Sayfa Sayıları: ss.1-21
  • Anahtar Kelimeler: Apostol type numbers and polynomials, combinatorial type numbers, Fubini type numbers and polynomials, generalized Apostol type numbers and polynomials, generating function, special numbers, Stirling type numbers
  • Akdeniz Üniversitesi Adresli: Evet

Özet

The goal of this paper is to define new families of unified and modified presentation of the Fubini numbers and polynomials with their generating functions. Using generating functions and their functional equations, many properties of these polynomials and numbers are presented. Relations among unified and modified presentation of the Fubini numbers and polynomials, Stirling type numbers, combinatorial type polynomials, and unified presentation of the generalized Bernoulli, Euler and Genocchi polynomials are given. Many novel identities and relations including these polynomials and numbers are also given. Moreover, new Hurwitz-Lerch type zeta functions, which interpolate unified and modified presentation of the Fubini numbers and polynomials at negative integers, are defined. Furthermore, suitable links of identities and relations, which are found in this paper, with those in earlier and future studies are indicated.