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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.
B. Sury
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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.
José L. Cereceda
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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 +2 more
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A New Generalization of Fibonacci Sequence & Extended Binet's Formula
Integers, 2009 AbstractConsider the Fibonacci ...
Marcia Edson, Omer Yayenie
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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.
Zoltán Sasvári
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Generalization of Binet's Gamma function formulas
Integral Transforms and Special Functions, 2012 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.
Gergő Nemes
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Binet’s Formula for the Tribonacci Sequence
The Fibonacci Quarterly, 1982The terms of a recursive sequence are usually defined by a recurrence procedure; that is, any term is the sum of preceding terms. Such a definition might not be entirely satisfactory, because the computation of any term could require the computation of ...
W. R. Spickerman
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Binet’s Formula for the Recursive Sequence of Order K
The Fibonacci Quarterly, 1984The terms of a recursive sequence are usually defined by a recurrence procedure; that is, any term is the sum of preceding terms. Such a definition might not be entirely satisfactory, because the computation of any term could require the computation of ...
W. R. Spickerman, R. N. Joyner
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