Results 141 to 150 of about 944 (165)

The k-Periodic Fibonacci Sequence and an Extended Binet's Formula

Integers, 2011
AbstractIt 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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Generalization of Binet's Gamma function formulas

Integral Transforms and Special Functions, 2013
Several representations for the logarithm of the Gamma function exist in the literature. There are four important expansions which bear the name of Binet. Hermite generalized Binet's first formula to the logarithm of the Gamma function with shifted argument.
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Binet's formula for generalized tribonacci numbers

International Journal of Mathematical Education in Science and Technology, 2015
In 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.
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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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Integral representations and complete monotonicity of remainders of the Binet and Stirling formulas for the gamma function

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Feng Qi, Bai-Ni Guo
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The Binet Formulas for the Pell and Pell-Lucas p-Numbers.

Ars Comb., 2007
In this paper, we define the Pell and Pell-Lucas p-numbers and derive the analytical formulas for these numbers. These formulas are similar to Bin et's formula for the classical Pell numbers.
Kocer, E. Gokcen, Tuglu, Naim
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Two-periodic ternary recurrences and their Binet-formula

2012
The two-periodic ternary recurrence sequence is defined by relations \(\gamma _n=a\gamma _{n-1}+b\gamma _{n-2}+c\gamma _{n-3}\) if \(n\) is even and \(\gamma _n=d\gamma _{n-1}+e\gamma _{n-2}+f\gamma _{n-3}\) if \(n\) is odd. In this paper, Cooper's approach [\textit{C. Cooper}, Congr.
Alp , M, Irmak , N, Szalay, László
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Quantum m*n-matrices and q-deformed Binet-Cauchy formula

Journal of Physics A: Mathematical and General, 1991
Summary: Quantum multiplicative matrices of size \(m\times n\) are introduced and studied. The \(q\)-generalization of the Binet-Cauchy formula is found.
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THE GRADED GENERALIZED FIBONACCI SEQUENCE AND BINET FORMULA

Far East Journal of Mathematical Sciences (FJMS), 2017
Won Sang Chung, Minji Han, Jae Yoon Kim
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New Proofs of Binet’s Formulas Using The Lucas Q-Matrix

Panamerican Mathematical Journal
The Fibonacci and Lucas sequences play a fundamental role in Number Theory and have deep connections with Linear Algebra and Matrix Theory. This paper explores an alternative approach to proving Binet’s formulas for these sequences using the Lucas -matrix, denoted by .
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