Results 1 to 10 of about 944 (165)
Extending generalized Fibonacci sequences and their binet-type formula [PDF]
Advances in Difference Equations, 2006 We study the extension problem of a given sequence defined by a finite order recurrence to a sequence defined by an infinite order recurrence with periodic coefficient sequence.
Saeki Osamu, Rachidi Mustapha
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Generalization of the 2-Fibonacci sequences and their Binet formula [PDF]
Notes on Number Theory and Discrete MathematicsWe will explore the generalization of the four different 2-Fibonacci sequences defined by Atanassov. In particular, we will define recurrence relations to generate each part of a 2-Fibonacci sequence, discuss the generating function and Binet formula of ...
Timmy Ma, Richard Vernon, Gurdial Arora
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The mathematics of generalized Fibonacci sequences: Binet's formula and identities [PDF]
Mathematica MoravicaThis 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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Some properties of extended remainder of binet’s first formula for logarithm of gamma function [PDF]
Mathematica Slovaca, 2010 Abstract 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 first formula for the logarithm of the gamma function and related functions.
Bai-Ni Guo, Feng Qi
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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.
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THE GENERALIZED BINET FORMULA, REPRESENTATION AND SUMS OF THE GENERALIZED ORDER-$k$ PELL NUMBERS
Taiwanese Journal of Mathematics, 2006 In this paper we give a new generalization of the Pell numbers in matrix representation. Also we extend the matrix representation and we show that the sums of the generalized order-k Pell numbers could be derived directly using this representation. Further we present some identities, the generalized Binet formula and combinatorial representation of the
Emrah Kilic
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A generalization of the Binet-Minc formula for the evaluation of permanents
Linear Algebra and Its Applications, 1988 The author presents a formula which coincides with the Binet-Minc formula for the evaluation of the permanent of the matrix \((a_{ij})\) which is presented in the polynomial \(\prod^{n}_{i=1}(\sum^{m}_{j=1}a_{ij}x_ j)\) where this formula is considered for the sum of the coefficients of monomials of the form \(x^{j_ 1}_{\ell_ 1}...x^{j_ p}_{\ell_ p ...
Akihiro Nishi
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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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Matrix Representation of Bi-Periodic Pell Sequence [PDF]
Journal of Mahani Mathematical Research, 2023 In this study, a generalization of the Pell sequence called bi-periodic Pell sequence is carried out to matrix theory. Therefore, we call this matrix sequence the bi-periodic Pell matrix sequence whose entries are bi-periodic Pell numbers.
Sukran UYGUN, Ersen Akıncı
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On the bivariate Padovan polynomials matrix [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 In this paper, we intruduce the bivariate Padovan sequence we examine its various identities. We define the bivariate Padovan polynomials matrix. Then, we find the Binet formula, generating function and exponential generating function of the bivariate ...
Orhan Dişkaya +2 more
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