Atıf İçin Kopyala
Uysal M., Özkan E., Shannon A. G.
JOURNAL OF SCIENCE AND ARTS, cilt.24, sa.4, ss.925-938, 2023 (ESCI)
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Yayın Türü:
Makale / Tam Makale
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Cilt numarası:
24
Sayı:
4
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Basım Tarihi:
2023
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Doi Numarası:
10.46939/j.sci.arts-23.4-a10
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Dergi Adı:
JOURNAL OF SCIENCE AND ARTS
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Derginin Tarandığı İndeksler:
Emerging Sources Citation Index (ESCI)
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Sayfa Sayıları:
ss.925-938
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Marmara Üniversitesi Adresli:
Hayır
Özet
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.