Results 1 to 10 of about 461 (158)

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

Mathematica Slovaca, 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
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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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On the Lichtenberg hybrid quaternions [PDF]

Mathematica Moravica
In this study, we define Lichtenberg hybrid quaternions. We give the Binet's formula, the generating functions, exponential generating functions and sum formulas of these quaternions. We find some relations between Jacobsthal hybrid quaternions, Mersenne
Morales Gamaliel
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A Training Algorithm for Locally Recurrent Neural Networks Based on the Explicit Gradient of the Loss Function [PDF]

Algorithms
In this paper, a new algorithm for the training of Locally Recurrent Neural Networks (LRNNs) is presented, which aims to reduce computational complexity and at the same time guarantee the stability of the network during the training.
Sara Carcangiu, Augusto Montisci
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Probabilistic approaches to exploring Binet's type formula for the Tribonacci sequence [PDF]

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
Najmeddine Attia, Skander Hachicha
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Multiparameter Quantum Cauchy-Binet Formulas [PDF]

Algebras and Representation Theory, 2020
The quantum Cayley-Hamilton theorem for the generator of the reflection equation algebra has been proven by Pyatov and Saponov, with explicit formulas for the coefficients in the Cayley-Hamilton formula. However, these formulas do not give an \emph{easy} way to compute these coefficients.
Karlin, Samuel, Rinott, Yosef
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Some properties and extended Binet’s formula for the class of bifurcating Fibonacci sequence

Ratio Mathematica
One of the generalizations of Fibonacci sequence is a -Fibonacci sequence, which is further generalized in several other ways, some by conserving the initial conditions and others by conserving the related recurrence relation.
Daksha Manojbhai Diwan, Devbhadra V Shah, Vandana R Patel   +2 more
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Elliptic curve and k-Fibonacci-like sequence

Scientific African, 2023
In this paper, we will introduce a modified k-Fibonacci-like sequence defined on an elliptic curve and prove Binet’s formula for this sequence. Moreover, we give a new encryption scheme using this sequence.
Zakariae Cheddour, Abdelhakim Chillali, Ali Mouhib   +2 more
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