Some New Families of Special Polynomials and Numbers Associated with Finite Operators

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ŞİMŞEK Y.

SYMMETRY-BASEL, vol.12, no.2, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 12 Issue: 2
  • Publication Date: 2020
  • Doi Number: 10.3390/sym12020237
  • Journal Name: SYMMETRY-BASEL
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Keywords: generating function, bernoulli numbers, euler numbers, stirling numbers, central factorial numbers, daehee numbers, changhee numbers, special functions, operators, p-adic integral, CENTRAL FACTORIAL NUMBERS, EULER NUMBERS, SUMS
  • Akdeniz University Affiliated: Yes

Abstract

The aim of this study was to define a new operator. This operator unify and modify many known operators, some of which were introduced by the author. Many properties of this operator are given. Using this operator, two new classes of special polynomials and numbers are defined. Many identities and relationships are derived, including these new numbers and polynomials, combinatorial sums, the Bernoulli numbers, the Euler numbers, the Stirling numbers, the Daehee numbers, and the Changhee numbers. By applying the derivative operator to these new polynomials, derivative formulas are found. Integral representations, including the Volkenborn integral, the fermionic p-adic integral, and the Riemann integral, are given for these new polynomials.