Results 11 to 20 of about 94,026 (132)
On complex Leonardo numbers [PDF]
Notes on Number Theory and Discrete Mathematics, 2022 In this study, we introduce the complex Leonardo numbers and give some of their properties including Binet formula, generating function, Cassini and d’Ocagne’s identities. Also, we calculate summation formulas for complex Leonardo numbers involving complex Fibonacci and Lucas numbers.
Adnan Karataş
openalex +4 more sources
, 2023 In this paper, we introduce a new generalization of Leonardo numbers, which are so-called Leonardo $p$-numbers. We investigate some basic properties of these numbers. We also define incomplete Leonardo $p$-numbers which generalize the incomplete Leonardo numbers.
Elif Tan, Ho-Hun Leung
openalex +2 more sources
Bicomplex Leonardo Numbers [PDF]
, 2022 In literature until today, many authors have studied special sequences in different number systems. In this paper, using the Leonardo numbers, we introduce the bicomplex Leonardo numbers. Also, we give some algebraic properties of bicomplex Leonardo numbers such as recurrence relation, generating function, Binet’s formula, D’Ocagne’s identity, Cassini ...
Fügen Torunbalcı Aydın
openalex +2 more sources
On New Banach Sequence Spaces Involving Leonardo Numbers and the Associated Mapping Ideal [PDF]
Journal of Function Spaces, 2022 In the present study, we have constructed new Banach sequence spaces ℓpL,c0L,cL, and ℓ∞L, where L=lv,k is a regular matrix defined by lv,k=lk/lv+2−v+2, 0≤k≤v,0, k>v, for all v,k=0,1,2,⋯, where l=lk is a sequence of Leonardo numbers.
Taja Yaying +3 more
doaj +2 more sources
Hybrinomials related to hyper-Leonardo numbers
Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics, 2023 In this paper, we define hybrinomials related to hyper-Leonardo numbers. We study some of their properties such as the recurrence relation and summation formulas. In addition, we introduce hybrid hyper Leonardo numbers.
Efruz Özlem MERSİN, Mustafa Bahşı
openalex +5 more sources
Generalized Horadam-Leonardo Numbers and Polynomials
Asian Journal of Advanced Research and Reports, 2023 In this study, we define and investigate some linear third order polynomials called the generalized Horadam-Leonardo polynomials (with its two special cases, namely), (r, s)-Horadam-Leonardo and (r, s)-Horadam-Leonardo-Lucas polynomials. We give Binet’s formulas, generating functions, Simson formulas, and the sumformulas for these polynomial sequences.
Yüksel Soykan
openalex +3 more sources
GAUSSIAN LEONARDO POLYNOMIALS AND APPLICATIONS OF LEONARDO NUMBERS TO CODING THEORY
Journal of Science and Arts, 2023 In this paper, we firstly introduce the Gaussian Leonardo polynomial sequences {GLe_n (x)}_(n=0)^∞ and we obtain Binet's formula, generating function of this sequence. Moreover, we define the matrix Gl(x) in the form of 3 x 3. Finally, we study on the coding and decoding applications of the Leonardo number by using the Leonardo matrix P.
Selime Beyza Özçevik, Abdullah Dertli
openalex +2 more sources
On Leonardo Pisano Hybrinomials
Mathematics, 2021 A generalization of complex, dual, and hyperbolic numbers has recently been defined as hybrid numbers. In this study, using the Leonardo Pisano numbers and hybrid numbers we investigate Leonardo Pisano polynomials and hybrinomials.
Ferhat Kürüz +2 more
exaly +3 more sources
A new perspective on bicomplex numbers with Leonardo number components
Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics, 2023 In the present paper, the bicomplex Leonardo numbers will be introduced with the use of Leonardo numbers and some important algebraic properties including recurrence relation, generating function, Catalan’s and Cassini’s identities, Binet’s formula, sum formulas will also be obtained.
Murat Turan +2 more
openalex +4 more sources
On $ 3 $-parameter generalized quaternions with higher order Leonardo numbers components
Electronic Research ArchiveIn this paper, a novel type of $ 3 $-parameter generalized quaternions ($ 3 $ -PGQs) is introduced, constructed from higher order Leonardo numbers and referred to as the higher order Leonardo $ 3 $-parameter generalized quaternions (shortly, higher order
Kübra GÜL
doaj +2 more sources