Title

ONE PARAMETER GENERALIZATIONS OF THE FIBONACCI AND LUCAS NUMBERS

Authors

Authors

M. E. H. Ismail

Comments

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Abbreviated Journal Title

Fibonacci Q.

Keywords

Mathematics

Abstract

We give one parameter generalizations of the Fibonacci and Lucas numbers denoted by {F(n)(theta)} and {L(n)(theta)}, respectively. We evaluate the Hankel determinants with entries {1/F(j+k+1)(theta) : 0 <= i, j <= n} and {1/L(j+k+1)(theta) : 0 <= i, j <= n}. We also find the entries in the inverse of {1/F(j+k+1)(theta) : 0 <= i, j <= n} and show that all its entries are integers. Some of the identities satisfied by the Fibonacci and Lucas numbers are extended to more general numbers. All integer solutions to three Diophantine equations related to the Pell equation are also found.

Journal Title

Fibonacci Quarterly

Volume

46-47

Issue/Number

2

Publication Date

1-1-2008

Document Type

Article

Language

English

First Page

167

Last Page

180

WOS Identifier

WOS:000266899100012

ISSN

0015-0517

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