On the harmonic and hyperharmonic Fibonacci numbers


TUĞLU N. , KIZILATEŞ C., KESİM S.

ADVANCES IN DIFFERENCE EQUATIONS, 2015 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume:
  • Publication Date: 2015
  • Doi Number: 10.1186/s13662-015-0635-z
  • Title of Journal : ADVANCES IN DIFFERENCE EQUATIONS
  • Keywords: harmonic number, hyperharmonic number, harmonic Fibonacci number, hyperharmonic Fibonacci number, matrix norm, CIRCULANT MATRICES, SPECTRAL NORMS, LUCAS-NUMBERS

Abstract

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.