Someone recently refered to Fib(n) = (sqrt(5)/5) ((1+sqrt(5))/2)^n - (1-sqrt(5))/2)^n) as the Binet form of the Fibonacci numbers. Would the term "Binet form" apply to any such explicit formula for a linear recurrence? - David W. Wilson "Truth is just truth -- You can't have opinions about the truth." - Peter Schickele, from P.D.Q. Bach's oratorio "The Seasonings"
`Binet' is a misnomer. The formula is in Euler's works, and probably was known even earlier. R. On Tue, 10 May 2005, David Wilson wrote:
Someone recently refered to
Fib(n) = (sqrt(5)/5) ((1+sqrt(5))/2)^n - (1-sqrt(5))/2)^n)
as the Binet form of the Fibonacci numbers. Would the term "Binet form" apply to any such explicit formula for a linear recurrence?
- David W. Wilson
"Truth is just truth -- You can't have opinions about the truth." - Peter Schickele, from P.D.Q. Bach's oratorio "The Seasonings"
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