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Bolyai Expansion


The Bolyai expansion of a real number x is a nested root of the form

 x=a_0-1+RadicalBox[{{a, _, 1}, +, RadicalBox[{{a, _, 2}, +, RadicalBox[{{a, _, 3}, +, ...}, m]}, m]}, m],

where 0<=a_k<=2^m-1.


See also

Continued Fraction, Nested Radical

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References

Martin, G. "The Unreasonable Effectualness of Continued Function Expansions." 17 Jun 2002. http://arxiv.org/abs/math.NT/0206166.Rényi, A. "Representations for Real Numbers and Their Ergodic Properties." Acta Math. Acad. Sci. Hungar. 8, 477-493, 1957.Trott, M. The Mathematica GuideBook for Programming. New York: Springer-Verlag, pp. 80-81, 2004. http://www.mathematicaguidebooks.org/.

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Bolyai Expansion

Cite this as:

Weisstein, Eric W. "Bolyai Expansion." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BolyaiExpansion.html

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