Results 1 to 10 of about 1,736,628 (188)

On Pell, Pell-Lucas, and balancing numbers [PDF]

Journal of Inequalities and Applications, 2018
In this paper, we derive some identities on Pell, Pell-Lucas, and balancing numbers and the relationships between them. We also deduce some formulas on the sums, divisibility properties, perfect squares, Pythagorean triples involving these numbers ...
Gul Karadeniz Gözeri
exaly   +10 more sources

Sums of Pell/Lucas Polynomials and Fibonacci/Lucas Numbers

Mathematics, 2022
Seven infinite series involving two free variables and central binomial coefficients (in denominators) are explicitly evaluated in closed form. Several identities regarding Pell/Lucas polynomials and Fibonacci/Lucas numbers are presented as consequences.
Dongwei Guo, Wenchang Chu
exaly   +4 more sources

On the spectral norm of r-circulant matrices with the Pell and Pell-Lucas numbers [PDF]

Journal of Inequalities and Applications, 2016
Let us define A = C r ( a 0 , a 1 , … , a n − 1 ) $A=C_{r}(a_{0},a_{1},\ldots,a_{n-1})$ to be a n × n $n \times n$ r-circulant matrix. The entries in the first row of A = C r ( a 0 , a 1 , … , a n − 1 ) $A=C_{r}(a_{0},a_{1},\ldots,a_{n-1})$ are a i = P i
Ramazan Turkmen
exaly   +4 more sources

On Bicomplex Pell and Pell-Lucas Numbers

Communications in Advanced Mathematical Sciences, 2018
In this paper, bicomplex Pell and bicomplex Pell-Lucas numbers are defined. Also, negabicomplex Pell and negabicomplex Pell-Lucas numbers are given. Some algebraic properties of bicomplex Pell and bicomplex Pell-Lucas numbers which are connected between ...
Fügen Torunbalcı Aydın
doaj   +5 more sources

Dual-Gaussian Pell and Pell-Lucas numbers

Cumhuriyet Science Journal, 2022
In this study, we define a new type of Pell and Pell-Lucas numbers which are called dual-Gaussian Pell and dual-Gaussian Pell-Lucas numbers. We also give the relationship between negadual-Gaussian Pell and Pell-Lucas numbers and dual-complex Pell
Hasan Gökbaş
doaj   +3 more sources

On Generalized Pell and Pell–Lucas Numbers [PDF]

Iranian Journal of Science and Technology, Transaction A: Science, 2019
In this paper, we introduce and study a new one-parameter generalization of Pell numbers. We describe their distinct properties also related to matrix representation.
Lucyna Trojnar-Spelina, Iwona Włoch
exaly   +2 more sources

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.
Hasan Gökbaş
doaj   +3 more sources

Reciprocal Formulae among Pell and Lucas Polynomials

Mathematics, 2022
Motivated by a problem proposed by Seiffert a quarter of century ago, we explicitly evaluate binomial sums with Pell and Lucas polynomials as weight functions.
Dongwei Guo, Mei Bai, Wenchang Chu
exaly   +3 more sources

Non-Newtonian Pell and Pell-Lucas numbers

Journal of New Results in Science
In the present paper, we introduce a new type of Pell and Pell-Lucas numbers in terms of non-Newtonian calculus, which we call non-Newtonian Pell and non-Newtonian Pell-Lucas numbers, respectively.
Tülay Yağmur
doaj   +4 more sources

Pell or Pell–Lucas numbers as concatenations of two repdigits in base b

Revista De La Real Academia De Ciencias Exactas, Fisicas Y Naturales - Serie A: Matematicas
17 ...
Salah Eddine Rihane, Alain Togbé, Alan Filipin   +2 more
exaly   +3 more sources