Results 1 to 10 of about 43 (41)

On generalized bihyperbolic Mersenne numbers [PDF]

Mathematica Bohemica, 2023
In this paper, a new generalization of Mersenne bihyperbolic numbers is introduced. Some of the properties of presented numbers are given. A general bilinear index-reduction formula for the generalized bihyperbolic Mersenne numbers is obtained.
Dorota Bród, Anetta Szynal-Liana
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On Some Properties of Bihyperbolic Numbers of The Lucas Type

Communications in Advanced Mathematical Sciences, 2023
To date, many authors in the literature have worked on special arrays in various computational systems. In this article, Lucas type bihyperbolic numbers were defined and their algebraic properties were examined. Bihyperbolic Lucas numbers were studied by
Fügen Torunbalcı Aydın
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On the Combinatorial Properties of Bihyperbolic Balancing Numbers [PDF]

Tatra Mountains Mathematical Publications, 2020
Abstract In this paper, we introduce bihyperbolic balancing and Lucas-balancing numbers. We give some of their properties, among others the Binet formula, Catalan, Cassini, d’Ocagne identities and the generating function.
Bród, Dorota, Szynal-Liana, Anetta, Włoch, Iwona   +2 more
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Topologies of Bihyperbolic Numbers

Mathematics, 2022
In this paper, we establish a correlation between the bihyperbolic numbers set and the semi-Euclidean space. There are three different norms on the semi-Euclidean space that allow us to define three different hypersurfaces on semi-Euclidean space. Hence, we construct some topological structures on these hypersurfaces called norm e, s, and t topologies.
Ana Savić, Merve Bilgin, Soley Ersoy, Marija Paunović   +3 more
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Two-parameter generalization of bihyperbolic Jacobsthal numbers

Proyecciones (Antofagasta), 2022
In this paper we define a two-parameter generalization of bihyperbolic Jacobsthal numbers. We give Binet formula, the generating functions and some identities for these numbers.
Dorota Bród, Anetta Szynal-Liana, Iwona Włoch   +2 more
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Gaussian-bihyperbolic Numbers Containing Pell and Pell-Lucas Numbers

Journal of Advanced Research in Natural and Applied Sciences, 2023
In this study, we define a new type of Pell and Pell-Lucas numbers which are called Gaussian-bihyperbolic Pell and Pell-Lucas numbers. We also define negaGaussian-bihyperbolic Pell and Pell-Lucas numbers. Moreover, we obtain Binet’s formulas, generating function formulas, d’Ocagne’s identities, Catalan’s identities, Cassini’s identities and some sum ...
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On generalized bihyperbolic third-order Jacobsthal polynomials [PDF]

Mathematica Bohemica
A new generalization of third-order Jacobsthal bihyperbolic polynomials is introduced. Some of the properties of presented polynomials are given. A general Vajda formula for the generalized bihyperbolic third-order Jacobsthal polynomials is obtained ...
Gamaliel Cerda-Morales
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On Mersenne Numbers and their Bihyperbolic Generalizations

Annales Mathematicae Silesianae
Abstract In this paper, we introduce Mersenne and Mersenne–Lucas bihyperbolic numbers, i.e. bihyperbolic numbers whose coefficients are consecutive Mersenne and Mersenne–Lucas numbers. Moreover, we study one parameter generalizations of Mersenne and Mersenne–Lucas bihyperbolic numbers.
Dorota Bród, Anetta Szynal-Liana
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An extended framework for bihyperbolic generalized Tribonacci numbers

Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics
The aim of this article is to identify and analyze a new type special number system which is called bihyperbolic generalized Tribonacci numbers (BGTN for short). For this purpose, we give both classical and several new properties such as; recurrence relation, Binet formula, generating function, exponential generating function, summation formulae ...
Nurten Gürses, Zehra İşbilir
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Bihyperbolic numbers of the Fibonacci type and triangular matrices (tables)

Azerbaijan Journal of Mathematics
Summary: In this paper, we compute paradeterminants and parapermanents of some triangular matrices that give bihyperbolic numbers of the Fibonacci type. Using connections between the paradeterminant of triangular matrix and the lower Hessenberg determinant, we also obtain the general term of these sequences.
Bednarz, P., Szynal-Liana, A.
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