ON DUAL BICOMPLEX BALANCING AND LUCAS-BALANCING NUMBERS
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Published:2023-12-30
Issue:4
Volume:24
Page:925-938
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ISSN:2068-3049
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Container-title:Journal of Science and Arts
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language:en
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Short-container-title:J. Sci. Arts
Author:
UYSAL MINE1, ÖZKAN ENGIN1, SHANNON ANTHONY G.2
Affiliation:
1. Erzincan Binali Yıldırım University, Faculty of Arts and Sciences, Department of Mathematics, Erzincan, Türkiye. 2. University of New South Wales, Warrane College, NSW 2033 Kensington, Australia.
Abstract
In this paper, dual bicomplex Balancing and Lucas-Balancing numbers
are defined, and some identities analogous to the classic properties of the Fibonacci
and Lucas sequences are produced. We give the relationship between these numbers
and Pell and Pell-Lucas numbers. From these, the basic bicomplex properties for
the norm and its conjugate of these numbers are also developed. These in turn lead
to the Binet formula, the generating functions and exponential generating functions,
which are important concepts for number sequences. The Cassini identity, which
is important for number sequences, actually emerged to solve the famous Curry
paradox. We calculated the Cassini, Catalan, Vajda and d’Ocagne identities for
these numbers.
Publisher
Valahia University of Targoviste - Journal of Science and Arts
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