On Harmonic Complex Balancing Numbers

Fatih Yılmaz (), Aybüke Ertaş and Jiteng Jia
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Fatih Yılmaz: Department of Mathematics, Haci Bayram Veli University, Ankara 06900, Turkey
Aybüke Ertaş: Department of Mathematics, Haci Bayram Veli University, Ankara 06900, Turkey
Jiteng Jia: Department of Mathematics and Statistics, Xidian University, Xi’an 710071, China

Mathematics, 2022, vol. 11, issue 1, 1-15

Abstract: In the present work, we define harmonic complex balancing numbers by considering well-known balancing numbers and inspiring harmonic numbers. Mainly, we investigate some of their basic characteristic properties such as the Binet formula and Cassini identity, etc. In addition, one type of symmetric matrix family whose entries are harmonic complex balancing numbers is constructed. Additionally, some linear algebraic properties are obtained. Furthermore, some inequalities are stated by exploiting the well-known inequalities between various matrix norms. Finally, we illustrate the results with some numerical examples.

Keywords: balancing number; Binet formula; Cassini identity; matrix norm; complex balancing number (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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