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Binet's Formula for Generalized Tribonacci Numbers
International Journal of Mathematical Education in Science and Technology, 2015In this note, we derive Binet's formula for the general term Tn of the generalized tribonacci sequence. This formula gives Tn explicitly as a function of the index n, the roots of the associated characteristic equation, and the initial terms T0, T1, and T2.
José Luis Cereceda
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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 (
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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
Dursun Taşci̧, Emrah Kilic
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The k-Periodic Fibonacci Sequence and an Extended Binet's Formula
Integers, 2011AbstractIt is well known that a continued fraction is periodic if and only if it is the representation of a quadratic ...
Marcia Edson, Scott Lewis, Omer Yayenie
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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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A New Generalization of Fibonacci Sequence & Extended Binet's Formula
Integers, 2009AbstractConsider the Fibonacci ...
Edson, Marcia, Yayenie, Omer
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Mathematics Magazine, 2004
Proof. The classical way to solve a linear equation system is by performing row operations: (i) add one row to another row, (ii) multiply a row with a nonzero scalar and (iii) exchange two rows. We show that the quotient in equation (1) will not change under row operations.
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Proof. The classical way to solve a linear equation system is by performing row operations: (i) add one row to another row, (ii) multiply a row with a nonzero scalar and (iii) exchange two rows. We show that the quotient in equation (1) will not change under row operations.
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An Elementary Proof of Binet's Formula for the Gamma Function
The American Mathematical Monthly, 1999(1999). An Elementary Proof of Binet's Formula for the Gamma Function. The American Mathematical Monthly: Vol. 106, No. 2, pp. 156-158.
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