On the Harmonic and Hyperharmonic Fibonacci Numbers
Naim Tuglu, Can K{\i}z{\i}late\c{s}, Seyhun Kesim
TL;DR
This paper explores the properties of harmonic and hyperharmonic Fibonacci numbers, deriving identities, formulas, and analyzing matrix norms involving these sequences.
Contribution
It introduces new formulas and identities for harmonic and hyperharmonic Fibonacci numbers, including spectral and Euclidean norms of related circulant matrices.
Findings
Derived combinatorial identities for harmonic and hyperharmonic Fibonacci numbers
Established formulas for finite sums of reciprocals of Fibonacci numbers
Calculated spectral and Euclidean norms of circulant matrices involving these 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 , which is finite sums of reciprocals of Fibonacci numbers. We obtain spectral and Euclidean norms of circulant matrices involving harmonic and hyperharmonic Fibonacci numbers.
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