ON PRODUCT DIFFERENCE FIBONACCI IDENTITIES

Melham, R

ON PRODUCT DIFFERENCE FIBONACCI IDENTITIES

Melham, R

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Publisher:: Walter de Gruyter GmbH & Co. KG
Publication Type:: Journal Article
Citation:: Integers, 2011, 11 pp. 1 - 8
Issue Date:: 2011-01

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Field	Value	Language
dc.contributor.author	Melham, R	en_US
dc.date.issued	2011-01	en_US
dc.identifier.citation	Integers, 2011, 11 pp. 1 - 8	en_US
dc.identifier.issn	1553-1732	en_US
dc.identifier.uri	http://hdl.handle.net/10453/17899
dc.description.abstract	Simson's identity is a well-known Fibonacci identity in which the difference of certain order 2 products has a particularly pleasing form. Other old and beautiful identities of a similar nature are attributed to Catalan, Gelin and Cesaro, and Tagiuri. Catalan's identity can be described as a family of product difference Fibonacci identities of order 2 with 1 parameter. In Section 2 of this paper we present four families of product difference Fibonacci identities that involve higher order products. Being self-dual, each of these families may be regarded as a higher order analogue of Catalan's identity. We also state two conjectures that give the form of similar families of arbitrary order. In the final section we give other interesting product difference Fibonacci identities.	en_US
dc.publisher	Walter de Gruyter GmbH & Co. KG	en_US
dc.relation.ispartof	Integers	en_US
dc.relation.isbasedon	10.1016/j.dam.2006.01.008	en_US
dc.title	ON PRODUCT DIFFERENCE FIBONACCI IDENTITIES	en_US
dc.type	Journal Article
utslib.citation.volume	11	en_US
utslib.for	0101 Pure Mathematics	en_US
utslib.for	0802 Computation Theory and Mathematics	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.consider-herdc	false	en_US
pubs.volume	11	en_US

Abstract:

Simson's identity is a well-known Fibonacci identity in which the difference of certain order 2 products has a particularly pleasing form. Other old and beautiful identities of a similar nature are attributed to Catalan, Gelin and Cesaro, and Tagiuri. Catalan's identity can be described as a family of product difference Fibonacci identities of order 2 with 1 parameter. In Section 2 of this paper we present four families of product difference Fibonacci identities that involve higher order products. Being self-dual, each of these families may be regarded as a higher order analogue of Catalan's identity. We also state two conjectures that give the form of similar families of arbitrary order. In the final section we give other interesting product difference Fibonacci identities.

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http://hdl.handle.net/10453/17899