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Bolyai Expansion

المؤلف:  Martin, G.

المصدر:  "The Unreasonable Effectualness of Continued Function Expansions." 17 Jun 2002. https://arxiv.org/abs/math.NT/0206166.

الجزء والصفحة:  ...

26-4-2020

1116

Bolyai Expansion

 

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

{{a, _, 1}, +, RadicalBox[{{a, _, 2}, +, RadicalBox[{{a, _, 3}, +, ...}, m]}, m]}, m], " src="https://mathworld.wolfram.com/images/equations/BolyaiExpansion/NumberedEquation1.gif" style="height:44px; width:230px" />

where .

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REFERENCES:

Martin, G. "The Unreasonable Effectualness of Continued Function Expansions." 17 Jun 2002. https://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. https://www.mathematicaguidebooks.org/.