On New Formulas of Fibonacci and Lucas Numbers Involving Golden Ratio Associated with Atomic Structure in Chemistry


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Battaloglu R., ŞİMŞEK Y.

SYMMETRY-BASEL, vol.13, no.8, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 13 Issue: 8
  • Publication Date: 2021
  • Doi Number: 10.3390/sym13081334
  • 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: Fibonacci and Lucas numbers, golden ratio, generating functions, Stirling numbers, periodic table, POLYNOMIALS, FAMILY
  • Akdeniz University Affiliated: Yes

Abstract

The main purpose of this paper is to give many new formulas involving the Fibonacci numbers, the golden ratio, the Lucas numbers, and other special numbers. By using generating functions for the special numbers with their functional equations method, we also give many new relations among the Fibonacci numbers, the Lucas numbers, the golden ratio, the Stirling numbers, and other special numbers. Moreover, some applications of the Fibonacci numbers and the golden ratio in chemistry are given.