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Nested Radical Constant

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NestedRadicalConstant

The nested radical constant is the constant defined by

C=sqrt(1+sqrt(2+sqrt(3+sqrt(4+sqrt(5+...)))))
(1)
=1.75793275...
(2)

(OEIS A072449).

No closed-form expression is known for this constant (Finch 2003, p. 8; S. Plouffe, pers. comm., Aug. 29, 2008).

See also

Nested Radical, Somos's Quadratic Recurrence Constant

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References

Borwein, J. M. and de Barra, G. "Nested Radicals." Amer. Math. Monthly 98, 735-739, 1991.Clawson, C. C. Mathematical Mysteries: The Beauty and Magic of Numbers Cambridge, MA: Perseus, pp. 142 and 299, 1996.Finch, S. R. "Analysis of a Radical Expansion." §1.2.1 in Mathematical Constants. Cambridge, England: Cambridge University Press, p. 8, 2003.Honsberger, R. More Mathematical Morsels. Washington, DC: Math. Assoc. Amer., pp. 140-144, 1991.Sloane, N. J. A. Sequence A072449 in "The On-Line Encyclopedia of Integer Sequences."Wells, D. The Penguin Dictionary of Curious and Interesting Numbers, rev. ed. Middlesex, England: Penguin Books, p. 30, 1997.Wolfram, S. A New Kind of Science. Champaign, IL: Wolfram Media, p. 915, 2002.

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Nested Radical Constant

Cite this as:

Weisstein, Eric W. "Nested Radical Constant." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/NestedRadicalConstant.html

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