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Cassini's Identity

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For F_n the nth Fibonacci number,

F_(n-1)F_(n+1)-F_n^2=(-1)^n.

This identity was also discovered by Simson (Coxeter and Greitzer 1967, p. 41; Coxeter 1969, pp. 165-168; Wells 1986, p. 62). It is a special case of Catalan's identity with r=1.

See also

d'Ocagne's Identity, Catalan's Identity, Fibonacci Number

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References

Coxeter, H. S. M. Introduction to Geometry, 2nd ed. New York: Wiley, 1969.Coxeter, H. S. M. and Greitzer, S. L. Geometry Revisited. Washington, DC: Math. Assoc. Amer., p. 41, 1967.Petkovšek, M.; Wilf, H. S.; and Zeilberger, D. A=B. Wellesley, MA: A K Peters, p. 12, 1996. http://www.cis.upenn.edu/~wilf/AeqB.html.Wells, D. The Penguin Dictionary of Curious and Interesting Numbers. Middlesex, England: Penguin Books, 1986.

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Cassini's Identity

Cite this as:

Weisstein, Eric W. "Cassini's Identity." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CassinisIdentity.html

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