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Dirichlet Convolution and the Binet Formula
2023Summary: The main aim of this note is to show that the set of closed triples of generalized Fibonacci arithmetic functions under the Dirichlet convolution is a singleton set. This unique Dirichlet convolution identity is the Binet Fibonacci number formula in terms of arithmetic functions and the Dirichlet convolution.
Schwab, Emil Daniel, Schwab, Gabriela
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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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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 ...
Edson, Marcia +2 more
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Generalization of Binet's Gamma function formulas
Integral Transforms and Special Functions, 2013Several 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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