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, cilt.13, sa.8, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 13 Sayı: 8
  • Basım Tarihi: 2021
  • Doi Numarası: 10.3390/sym13081334
  • Dergi Adı: SYMMETRY-BASEL
  • Derginin Tarandığı İndeksler: 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
  • Anahtar Kelimeler: Fibonacci and Lucas numbers, golden ratio, generating functions, Stirling numbers, periodic table, POLYNOMIALS, FAMILY
  • Akdeniz Üniversitesi Adresli: Evet

Özet

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.