WebKızılateş, C., & Kone, T. (2024). On higher order Fibonacci hyper complex numbers. Chaos, Solitons & Fractals, 148, 111044. doi:10.1016/j.chaos.2024.111044 WebIn this paper, we study norms of circulant and r -circulant matrices involving harmonic Fibonacci and hyperharmonic Fibonacci numbers. We obtain inequalities by using matrix norms. MSC: Primary 15A60; secondary 15B05; 11B39 Keywords: hyperharmonic Fibonacci number; r -Circulant matrix; matrix norm 1 Introduction
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WebThe Fibonacci and Lucas numbers and are entire analytical functions of that are defined over the whole complex -plane: Periodicity. The Fibonacci and Lucas numbers and do … Webratio, and hyper-numbers such as hyper-Fibonacci, hyper-Lucas,andhyper-Pellnumbers.Forthis,we rstlyinvestigate the ratio / 1 while by using a symmetric algorithm obtained by the recurrence relation = 1 + 1. 2. Main Results eorem . Let the sequence be as in (). If lim ( / 1)=!,thenfor 0 lim effects of a earthquake
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WebThe generating functions of hyper-Fibonacci and hyper-Lucasnumbersare[4]: X1 n=0 F(r) nt n= t (1 t t2)(1 t)r ; X1 n=0 L(r) nt n= 2 t (1 t t2)(1 t)r : Also,thehyper-Fibonacciandhyper-Lucasnumbershavetherecurrencerelations F(r) n=F (r) n 1+F (r 1) nandL (r) n=L (r) n 1+L (r 1) n,respectively. Thefirstfewvalues ofF(r) nandL Webn 0 are the classical Fibonacci and Lucas numbers respectively. Hyper-Fibonacci numbers and hyper-Lucas numbers satisfy many interesting number-theo-retical and … http://ir.buu.ac.th/dspace/bitstream/1513/158/1/61910070.pdf effects of ageing health and social care