Hyperbolic Horadam Functions

Bahşi, Mustafa; Solak, Süleyman

doi:10.35378/gujs.441422

Cited by 2 publications

(7 citation statements)

References 11 publications

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“…Definition 2.1. Hyperbolic Horadam hybrid function is defined as 3 , α and β are as in equation (3).…”

Section: Resultsmentioning

confidence: 99%

“…where A = b − aβ and B = b − aα [7]. Considering the equality αβ = −q, the Binet formula in equation ( 6) is rewritten as [3] W…”

Section: Introductionmentioning

confidence: 99%

“…Considering the similarity between the Binet formulas in equation ( 7) and generalized hyperbolic functions in equation ( 15), Bahs ¸i and Solak [3] defined the hyperbolic Horadam functions which are called hyperbolic Horadam sine and cosine functions as…”

Section: Introductionmentioning

confidence: 99%

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Hyperbolic Horadam hybrid functions

MERSİN¹

2023

NNTDM

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The aim of this paper is to introduce the hybrid form of the hyperbolic Horadam function and to investigate some of its properties such as the generating function. Another aim is to define hyperbolic Horadam hybrid sine and cosine functions and their symmetrical forms. For newly defined functions, some properties such as the recursive relations, derivatives, Cassini and De Moivre type identities are examined. In addition, the quasi-sine Horadam hybrid function and three-dimensional Horadam hybrid spiral are defined.

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“…Definition 2.1. Hyperbolic Horadam hybrid function is defined as 3 , α and β are as in equation (3).…”

Section: Resultsmentioning

confidence: 99%

“…where A = b − aβ and B = b − aα [7]. Considering the equality αβ = −q, the Binet formula in equation ( 6) is rewritten as [3] W…”

Section: Introductionmentioning

confidence: 99%

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Hyperbolic Horadam hybrid functions

MERSİN¹

2023

NNTDM

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“…Using the Binet formulas (2.2) and (2.3), hyperbolic Fibonacci and Lucas functions and their symmetrical forms have been defined [12,15,17]. Using the Binet formula (2.1), Bahşi and Solak [3] have defined hyperbolic Horadam sine and cosine functions for the continuous variable x:…”

Section: Hyperbolic Horadam Functionsmentioning

confidence: 99%

“…has been defined in [3], where x ∈ R and i 2 = −1. The matrix form of the three-dimensional Horadam spiral is:…”

Section: The Matrix Form Of the Metallic Shofarsmentioning

confidence: 99%

On the hyperbolic Horadam matrix functions

Bahşi

MERSİN

2022

Hacettepe Journal of Mathematics and Statistics

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In this study, we introduce a new class of the hyperbolic matrix functions which are called symmetrical hyperbolic Horadam sine and cosine matrix functions and we present some hyperbolic and recursive properties of these new matrix functions. In addition, we introduce quasi-sine Horadam matrix function and also define the matrix form of the metallic shofars that related to the hyperbolic Horadam sine and hyperbolic Horadam cosine matrix functions.

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Hyperbolic Horadam Functions

Abstract: Highlights• We define hyperbolic Horadam functions.• We present their hyperbolic and recursive properties.• Our findings generalize the previous studies.

Cited by 2 publications

References 11 publications

Hyperbolic Horadam hybrid functions

Hyperbolic Horadam hybrid functions

On the hyperbolic Horadam matrix functions

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