Generalized order-\(k\) Fibonacci and Lucas functions
type: Item
instance of: scholarly article
title: Generalized order-\(k\) Fibonacci and Lucas functions
zbMATH Open document ID: 1239.11018
DOI: 10.1216/RMJ-2008-38-6-1991
published in: Rocky Mountain Journal of Mathematics
publication date: 2009-04-07T00:00:00Z
review text: For any real number \(x\) and \(1\leq i\leq k\), the authors define and study the function \[ F(i,k,x)= \sum^\infty_{t=0} (g^i_t/t!)x^t, \] where \[ g^i_n= \sum^k_{j=1} g^i_{n-j}\quad (n> 0,\;1\leq i\leq k), \] and \(g^i_n= 1\) if \(i= 1-n\) and \(0\) otherwise \((1-k\leq n\leq 0)\). They name \(F(i,k,x)\) generalized order-\(k\) Fibonacci function. They also define and study a function \(L(i,k,x)\), which they call generalized order-\(k\) Lucas function.
reviewed by: Andreas N. Philippou
Mathematics Subject Classification ID: 11B39
Mathematics Subject Classification ID: 11B37
zbMATH DE Number: 5541308
zbMATH Keywords: generalized order-\(k\) Fibonacci and Lucas numbers
zbMATH Keywords: Fibonacci and Lucas functions
author: Emrah Kılıç
author: Dursun Tasci
MaRDI profile type: Publication
cites work: Q5548431
cites work: Q3325804
cites work: On the generalized order-\(k\) Fibonacci and Lucas numbers
cites work: Q4431527
cites work: Generalized Fibonacci Numbers and Associated Matrices
cites work: On the order-\(k\) generalized Lucas numbers
cites work: Bounds for characteristic roots of matrices
cites work: Q4692934
full work available at URL: rmj-2008-38-6-1991
OpenAlex ID: W2045499580
description: scientific article; zbMATH DE number 5541308