One-parameter generalization of the bihyperbolic Jacobsthal numbers

Bród, Dorota; Szynal‐Liana, Anetta; Włoch, Iwona

doi:10.1142/s1793557123500754

Asian-European J. Math.

2022

DOI: 10.1142/s1793557123500754

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One-parameter generalization of the bihyperbolic Jacobsthal numbers

Dorota Bród

Anetta Szynal‐Liana

Iwona Włoch

Abstract: In this paper, we introduce and study a one-parameter generalization of bihyperbolic Jacobsthal numbers. We give some identities and the generating function for these numbers.

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2024

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An extended framework for bihyperbolic generalized Tribonacci numbers

Gürses,

İşbilir

2024

Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.

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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, matrix formula, and special determinant equations of BGTN . Also, the system of BGTN is quite a big family and includes several type special cases with respect to initial values and $r,~ s, ~t$ values, we give the subfamilies and special cases of it. In addition to these, we construct some numerical algorithms including recurrence relation and special two types determinant equations related to calculating the terms of this new type special number system. Then, we examine several properties by taking two special cases and including some illustrative numerical examples.

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An extended framework for bihyperbolic generalized Tribonacci numbers

Gürses,

İşbilir

2024

Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.

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One-parameter generalization of the bihyperbolic Jacobsthal numbers

Abstract: In this paper, we introduce and study a one-parameter generalization of bihyperbolic Jacobsthal numbers. We give some identities and the generating function for these numbers.

Cited by 1 publication

References 13 publications

An extended framework for bihyperbolic generalized Tribonacci numbers

An extended framework for bihyperbolic generalized Tribonacci numbers

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