ONE PARAMETER GENERALIZATIONS OF THE FIBONACCI AND LUCAS NUMBERS

    Authors

    M. E. H. Ismail

    Comments

    Authors: contact us about adding a copy of your work at STARS@ucf.edu

    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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