Some theorems involving powers of generalized Fibonacci numbers at non-equidistant points

Bruckman, PS; Melham, RS

Some theorems involving powers of generalized Fibonacci numbers at non-equidistant points

Bruckman, PS Melham, RS

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Publication Type:: Journal Article
Citation:: Fibonacci Quarterly, 2007, 45 (3), pp. 208 - 220
Issue Date:: 2007-08-01

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Field	Value	Language
dc.contributor.author	Bruckman, PS	en_US
dc.contributor.author	Melham, RS	en_US
dc.date.issued	2007-08-01	en_US
dc.identifier.citation	Fibonacci Quarterly, 2007, 45 (3), pp. 208 - 220	en_US
dc.identifier.issn	0015-0517	en_US
dc.identifier.uri	http://hdl.handle.net/10453/8245
dc.description.abstract	The paper begins with a brief review of the generalized Fibonacci polynomials, satisfying the recurrence : Gn+2(x) = xG n+1(x) + Gn(x), with arbitrary initial values. After these introductory remarks, the paper points out that the plethora of identities that abound in the literature and that are associated with these sequences are based on evenly-spaced values of the subscripts. As implied in the title, the paper generalizes such identities by stating and proving various theorems and corollaries, giving identities satisfied by the mth powers of the Gn(x)'s (or special values thereof). In these generalizations, m is fixed, but the different values of n are arbitrary and therefore not equidistant, in general. Essentially, two main theorems of this nature are presented in this paper, of which the others are either corollaries or auxiliary results leading thereto.	en_US
dc.relation.ispartof	Fibonacci Quarterly	en_US
dc.subject.classification	General Mathematics	en_US
dc.title	Some theorems involving powers of generalized Fibonacci numbers at non-equidistant points	en_US
dc.type	Journal Article
utslib.citation.volume	3	en_US
utslib.citation.volume	45	en_US
utslib.for	0101 Pure Mathematics	en_US
utslib.for	0103 Numerical and Computational Mathematics	en_US
utslib.for	0199 Other Mathematical Sciences	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Science
utslib.copyright.status	open_access
pubs.issue	3	en_US
pubs.publication-status	Published	en_US
pubs.volume	45	en_US

Abstract:

The paper begins with a brief review of the generalized Fibonacci polynomials, satisfying the recurrence : Gn+2(x) = xG n+1(x) + Gn(x), with arbitrary initial values. After these introductory remarks, the paper points out that the plethora of identities that abound in the literature and that are associated with these sequences are based on evenly-spaced values of the subscripts. As implied in the title, the paper generalizes such identities by stating and proving various theorems and corollaries, giving identities satisfied by the mth powers of the Gn(x)'s (or special values thereof). In these generalizations, m is fixed, but the different values of n are arbitrary and therefore not equidistant, in general. Essentially, two main theorems of this nature are presented in this paper, of which the others are either corollaries or auxiliary results leading thereto.

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http://hdl.handle.net/10453/8245