On the harmonic and hyperharmonic Fibonacci numbers

TUĞLU N., KIZILATEŞ C., KESİM S.

ADVANCES IN DIFFERENCE EQUATIONS, 2015 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2015
  • Doi Numarası: 10.1186/s13662-015-0635-z
  • Dergi Adı: ADVANCES IN DIFFERENCE EQUATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: harmonic number, hyperharmonic number, harmonic Fibonacci number, hyperharmonic Fibonacci number, matrix norm, CIRCULANT MATRICES, SPECTRAL NORMS, LUCAS-NUMBERS
  • Gazi Üniversitesi Adresli: Evet

Özet

In this paper, we study the theory of the harmonic and the hyperharmonic Fibonacci numbers. Also, we get some combinatoric identities like as harmonic and hyperharmonic numbers and we obtain some useful formulas for F-n, which is concerned with finite sums of reciprocals of Fibonacci numbers. We obtain the spectral and Euclidean norms of circulant matrices involving harmonic and hyperharmonic Fibonacci numbers.