Results 31 to 40 of about 916 (171)

On a generalization of the Pell sequence [PDF]

Mathematica Bohemica, 2021
The Pell sequence $(P_n)_{n=0}^{\infty}$ is the second order linear recurrence defined by $P_n=2P_{n-1}+P_{n-2}$ with initial conditions $P_0=0$ and $P_1=1$.
Jhon J. Bravo, Jose L. Herrera, Florian Luca   +2 more
doaj   +1 more source

The complex-type Pell p-numbers [PDF]

Notes on Number Theory and Discrete Mathematics
In this paper, we define the complex-type Pell p-numbers and give the generating matrix of these defined numbers. Then, we produce the combinatorial representation, the generating function, the exponential representation and the sums of the complex-type ...
Yeşim Aküzüm, Hüseyin Aydın, Ömür Deveci   +2 more
doaj   +1 more source

A quantum calculus framework for Gaussian Fibonacci and Gaussian Lucas quaternion numbers [PDF]

Notes on Number Theory and Discrete Mathematics
In order to investigate the relationship between Gaussian Fibonacci numbers and quantum numbers and to develop both a deeper theoretical understanding in this study, q-Gaussian Fibonacci, q-Gaussian Lucas quaternions and polynomials are taken with ...
Bahar Kuloğlu
doaj   +1 more source

On Some Properties of Bihyperbolic Numbers of The Lucas Type

Communications in Advanced Mathematical Sciences, 2023
To date, many authors in the literature have worked on special arrays in various computational systems. In this article, Lucas type bihyperbolic numbers were defined and their algebraic properties were examined. Bihyperbolic Lucas numbers were studied by
Fügen Torunbalcı Aydın
doaj   +1 more source

Binet's second formula, Hermite's generalization, and two related identities

Open Mathematics, 2023
Abstract Legendre was the first to evaluate two well-known integrals involving sines and exponentials. One of these integrals can be used to prove Binet’s second formula for the logarithm of the gamma function. Here, we show that the other integral leads to a specific case of Hermite’s generalization of Binet’s formula.
openaire   +2 more sources

Horadam Octonions

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2017
In this paper, first we define Horadam octonions by Horadam sequence which is a generalization of second order recurrence relations. Also, we give some fundamental properties involving the elements of that sequence.
Karataş Adnan, Halici Serpil
doaj   +1 more source

On a generalization of the Gadovan numbers [PDF]

Mathematica Moravica
In this paper, we define (k, l)-Gadovan numbers. We give the Binet-like formula, the generating functions, the exponential generating function of the (k, l)-Gadovan numbers. Also, we derive Cassinilike identity, Catalan-like identity, Vajda-like identity,
Özkan Engın, Eser Engın, Uysal Mıne
doaj   +1 more source

On fourth-order jacobsthal quaternions

Journal of Mathematical Sciences and Modelling, 2018
In this paper, we present for the first time a sequence of quaternions of order 4 that we will call the fourth-order Jacobsthal and the fourth-order Jacobsthal-Lucas quaternions. In particular, we are interested in the generating function, Binet formula,
Gamaliel Cerda-morales
doaj   +1 more source

On an application of Binet’s second formula

Proceedings of the American Mathematical Society, 2017
Let \(f(x)= \int^\infty_0 ((\sin t)/(t+ x))\,dt\) and \(g(x)= \int^\infty_0 ((\cos t)/(t+ x))\,dt\). The author proves the following representation formulas: \[ \begin{aligned} f(2\pi) &= \pi \sum^\infty_{n=1} {\mu(n)\over n}\,\Biggl(\log\Gamma(nx)- nx\log(nx)+ nx-{1\over 2}\log\Biggl({2\pi\over nx}\Biggr)\Biggr)\qquad\text{and}\\ g(2\pi) &= {1\over 2}\
openaire   +1 more source

Massive Spanning Forests on the Complete Graph: Exact Distribution and Local Limit

Random Structures &Algorithms, Volume 68, Issue 2, March 2026.
ABSTRACT We provide new exact formulas for the distribution of massive spanning forests on the complete graph, which give also a new outlook on the celebrated special case of the uniform spanning tree. As a corollary we identify their local limit. This generalizes a well‐known theorem of Grimmett on the local limit of uniform spanning trees on the ...
Matteo D'Achille, Nathanaël Enriquez, Paul Melotti   +2 more
wiley   +1 more source