Continued Square Root
Expressions of the form
Herschfeld (1935) proved that a continued square root of Real Nonnegative terms convergesIff
is bounded. He extended this result to arbitrary Powers (which includecontinued square roots and Continued Fractions as well), which is known as Herschfeld'sConvergence Theorem.See also Continued Fraction, Herschfeld's Convergence Theorem, Nested Radical, Square Root
References
Herschfeld, A. ``On Infinite Radicals.'' Amer. Math. Monthly 42, 419-429, 1935. Pólya, G. and Szegö, G. Problems and Theorems in Analysis, Vol. 1. New York: Springer-Verlag, 1997. Sizer, W. S. ``Continued Roots.'' Math. Mag. 59, 23-27, 1986.
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