Nested Radical Constant

The nested radical constant is the constant defined by

			(1)
			(2)

(OEIS A072449).

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

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.