Results 21 to 30 of about 1,163,634 (140)

Stirling’s Original Asymptotic Series from a Formula Like One of Binet’s and its Evaluation by Sequence Acceleration [PDF]

Experimental Mathematics, 2018
We give an apparently new proof of Stirling’s original asymptotic formula for the behavior of for large z. Stirling’s original formula is not the formula widely known as “Stirling’s formula”, which was actually due to De Moivre.
Robert M Corless, Leili Rafiee Sevyeri
semanticscholar   +1 more source

Extending generalized Fibonacci sequences and their binet-type formula [PDF]

Advances in Difference Equations, 2006
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Saeki Osamu, Rachidi Mustapha
openaire   +2 more sources

Dual Jacobsthal Quaternions

Communications in Advanced Mathematical Sciences, 2020
In this paper, dual Jacobsthal quaternions were defined. Also, the relations between dual Jacobsthal quaternions which connected with Jacobsthal and Jacobsthal-Lucas numbers were investigated. Furthermore, Binet's formula, Honsberger identity, D'ocagne'
Fügen Torunbalcı Aydın
doaj   +1 more source

Some identities of bivariate Pell and bivariate Pell-Lucas polynomials

Journal of Amasya University the Institute of Sciences and Technology, 2023
In this paper, we obtain some identities for the bivariate Pell polynomials and bivariate Pell-Lucas polynomials. We establish some sums and connection formulas involving them.
Yashwant Panwar
doaj   +1 more source

Higher-Order Jacobsthal–Lucas Quaternions

Axioms, 2022
In this work, we define higher-order Jacobsthal–Lucas quaternions with the help of higher-order Jacobsthal–Lucas numbers. We examine some identities of higher-order Jacobsthal–Lucas quaternions. We introduce their basic definitions and properties.
Mine Uysal, Engin Özkan
doaj   +1 more source

Hyperbolic Fibonacci Sequence

Universal Journal of Mathematics and Applications, 2019
In this paper, we investigate the hyperbolic Fibonacci sequence and the hyperbolic Fibonacci numbers. Furthermore, we give recurrence relations, the golden ratio and Binet's formula for the hyperbolic Fibonacci sequence and Lorentzian inner product ...
Fügen Torunbalcı Aydın
doaj   +1 more source

On a New One Parameter Generalization of Pell Numbers

Annales Mathematicae Silesianae, 2019
In this paper we present a new one parameter generalization of the classical Pell numbers. We investigate the generalized Binet’s formula, the generating function and some identities for r-Pell numbers.
Bród Dorota
doaj   +1 more source

An Elementary Proof of the Generalization of the Binet Formula for $k$-bonacci Numbers

CoRR, 2022
We present an elementary proof of the generalization of the $k$-bonacci Binet formula, a closed form calculation of the $k$-bonacci numbers using the roots of the characteristic polynomial of the $k$-bonacci recursion.
Harold R. Parks, Dean C. Wills
openaire   +2 more sources

Bivariate Leonardo polynomials and Riordan arrays [PDF]

Notes on Number Theory and Discrete Mathematics
In this paper, bivariate Leonardo polynomials are defined, which are closely related to bivariate Fibonacci polynomials. Bivariate Leonardo polynomials are generalizations of the Leonardo polynomials and Leonardo numbers.
Yasemin Alp, E. Gökçen Koçer
doaj   +1 more source

Theory of Binet formulas for Fibonacci and Lucas p-numbers

Chaos, Solitons & Fractals, 2006
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Stakhov, Alexey, Rozin, Boris
  +10 more sources