Results 21 to 30 of about 1,056,912 (212)
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.
Matthias Floré
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Linear Algebra and its Applications, 1989 The author gives a combinatorial proof of Muir's identity between permanents and determinants and of the Cauchy-Binet formula. Some related identities are also commented on.
Samuel Karlin, Yosef Rinott
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Probabilistic approaches to exploring Binet's type formula for the Tribonacci sequence
AIMS MathematicsThis 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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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.
R. Boyack
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A simplified Binet formula for k-generalized Fibonacci numbers [PDF]
, 2009 We present a particularly nice Binet-style formula that can be used to produce the k-generalized Fibonacci numbers (that is, the Tribonaccis, Tetranaccis, etc). Furthermore, we show that in fact one needs only take the integer closest to the first term of this Binet-style formula to generate the desired sequence.
Gregory P. Dresden
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A multilinear algebra proof of the Cauchy-Binet formula and a multilinear version of Parseval's identity [PDF]
, 2013 We give a short proof of the Cauchy-Binet determinantal formula using multilinear algebra by first generalizing it to an identity {\em not} involving determinants.
Konstantopoulos, Takis
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An Elementary Proof of the Generalization of the Binet Formula for $k$-bonacci Numbers [PDF]
arXiv.org, 2022 Harold R. Parks, Dean C. Wills
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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}\
Ruiming Zhang
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A combined approach to Perrin and Padovan hybrid sequences [PDF]
Heliyon, 2021 Recently, there has been huge interest to a new numeric set, which brings together three numerical systems: complex, hyperbolic and dual numbers, called as hybrid number.
Seyyed H. Jafari Petroudi +3 more
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Binet’s formula for operator-valued recursive sequences and the operator moment problem
Extracta MathematicaeWe 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 +3 more
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