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# Binet's Formula

Binet's formula is an equation which gives the th Fibonacci number as a difference of positive and negative th powers of the golden ratio . It can be written as

 (1) (2)

Binet's formula is a special case of the Binet form with It was derived by Binet in 1843, although the result was known to Euler, Daniel Bernoulli, and de Moivre more than a century earlier.

Binet Forms, Binet's Log Gamma Formulas, Fibonacci Number, Linear Recurrence Equation

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## References

Livio, M. The Golden Ratio: The Story of Phi, the World's Most Astonishing Number. New York: Broadway Books, p. 108, 2002.Séroul, R. Programming for Mathematicians. Berlin: Springer-Verlag, p. 21, 2000.Wells, D. The Penguin Dictionary of Curious and Interesting Numbers. Middlesex, England: Penguin Books, p. 62, 1986.

## Cite this as:

Weisstein, Eric W. "Binet's Formula." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BinetsFormula.html