Results 1 to 10 of about 1,029,498 (122)

Some properties of extended remainder of Binet's first formula for logarithm of gamma function [PDF]

, 2010
In the paper, we extend Binet's first formula for the logarithm of the gamma function and investigate some properties, including inequalities, star-shaped and sub-additive properties and the complete monotonicity, of the extended remainder of Binet's ...
Guo, Bai-Ni, Qi, Feng
core   +4 more sources

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

Open Mathematics, 2023
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.
Boyack Rufus
doaj   +2 more sources

A New Generalization of Leonardo Sequences: Biperiodic Leonardo Sequence

Journal of Mathematics
In this study, we define a new type of number sequence called biperiodic Leonardo sequence by the recurrence relation Lena,b=aLen−1+Len−2+1 (for even n) and Lena,b=bLen−1+Len−2+1 (for odd n) with the initial conditions Le0a,b=Le1a,b=1.
Hasan Gökbaş
doaj   +3 more sources

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

Experimental Mathematics, 2019
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
openalex   +2 more sources

Quadratic Approximation of Generalized Tribonacci Sequences

Discussiones Mathematicae - General Algebra and Applications, 2018
In this paper, we give quadratic approximation of generalized Tribonacci sequence {Vn}n≥0 defined by Vn = rVn−1 + sV n−2 + tV n−3 (n ≥ 3) and use this result to give the matrix form of the n-th power of a companion matrix of {Vn}n≥0. Then we re-prove the
Cerda-Morales Gamaliel
doaj   +2 more sources

Probabilistic approaches to exploring Binet's type formula for the Tribonacci sequence

AIMS Mathematics
This paper presents a detailed procedure for deriving a Binet's type formula for the Tribonacci sequence $ \{ {\mathsf T}_n\} $. We examine the limiting distribution of a Markov chain that encapsulates the entire sequence $ \{ {\mathsf T}_n\} $, offering
Skander Hachicha, Najmeddine Attia
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Hyper-Dual Leonardo Quaternions

Journal of New Theory
In this paper, hyper-dual Leonardo quaternions are defined and studied. Some basic properties of the hyper-dual Leonardo quaternions, including their relationships with the hyper-dual Fibonacci quaternions and hyper-dual Lucas quaternions, are analyzed ...
Tülay Yağmur
doaj   +2 more sources

On a unified approach to homogeneous second-order linear difference equations with constant coefficients and some applications

Special Matrices
In this article, we establish a new closed formula for the solution of homogeneous second-order linear difference equations with constant coefficients by using matrix theory.
Kaddoura Issam, Mourad Bassam
doaj   +2 more sources

A new approach to Leonardo number sequences with the dual vector and dual angle representation

AIMS Mathematics
In this paper, we introduce dual numbers with components including Leonardo number sequences. This novel approach facilitates our understanding of dual numbers and properties of Leonardo sequences.
Faik Babadağ, Ali Atasoy
doaj   +2 more sources

On an application of Binet’s second formula

, 2017
Ruiming Zhang
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