Results 1 to 10 of about 1,163,634 (140)

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   +3 more sources

On an application of Binet’s second formula

Proceedings of the American Mathematical Society, 2017
In this work we apply the second Binet formula for Euler’s gamma function Γ (
Ruiming Zhang
semanticscholar   +2 more sources

Binet’s formula for operator-valued recursive sequences and the operator moment problem

Extracta Mathematicae
We derive a Binet-type formula for operator-valued sequences satisfying linear recurrence relations, extending the classical scalar case to the setting of bounded operators on Hilbert spaces.
A. Ech-charyfy, A. Ghanmi, K. Idrissi, A. Salhi   +3 more
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New results for the Fibonacci sequence using Binet's formula

International Mathematical Forum, 2018
Let k ≥ 1 and h = 0, . . . , k − 1. In this note we study the monotonicity of the sequences (Fkn+h) , where Fn denotes the n-th Fibonacci number. In particular, we prove that the sequences (F2n) 1/n and (F2n+1) 1/n are strictly increasing for n ≥ 1.
Reza Farhadian, R. Jakimczuk
semanticscholar   +2 more sources

The mathematics of generalized Fibonacci sequences: Binet's formula and identities [PDF]

Mathematica Moravica
This article considers a generalized Fibonacci sequence {Vn} with general initial conditions, V0 = a, V1 = b, and a versatile recurrence relation Vn = pVn-1 + qVn-2, where n ≥ 2 and a, b, p and q are any non-zero real numbers. The generating function and
Verma K.L.
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Floor and ceiling functions for Pell numbers [PDF]

Notes on Number Theory and Discrete Mathematics
The analytical study of the Pell number and the role of floor and ceiling functions into their computation is examined. Closed expressions of Pell numbers were initially derived using Binet's formula, followed by an asymptotic behavior study of the ...
İsmail Sulan, Mustafa Aşçı
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Some properties of extended remainder of binet’s first formula for logarithm of gamma function [PDF]

Mathematica Slovaca, 2009
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 ...
Feng Qi (祁锋), Bai-Ni Guo (郭白妮)
semanticscholar   +4 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 { T n } . We examine the limiting distribution of a Markov chain that encapsulates the entire sequence { T n } , offering insights into its ...
S. Hachicha, N. Attia
semanticscholar   +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
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New Results on Negative-Indexed Pell Numbers via Matrix Methods

Cumhuriyet Science Journal
In this study, we investigate the Pell and Pell–Lucas numbers sequences and construct matrices whose elements are defined using negative indices of these sequences through Binet’s formula. Identities involving negative-indexed Pell and Pell–Lucas numbers
İbrahim Gökcan, Ümmügülsün Çağlayan, Ali Hikmet Değer   +2 more
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