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Continued radicals

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Abstract

If a 1,a 2,…,a n are nonnegative real numbers and \(f_{j}(x)=\sqrt{a_{j}+x}\) , then f 1○f 2○⋅⋅⋅○f n (0) is a nested radical with terms a 1,…,a n . If it exists, the limit as n→∞ of such an expression is a continued radical. We consider the set of real numbers S(M) representable as a continued radical whose terms a 1,a 2,… are all from a finite set M. We give conditions on the set M for S(M) to be (a) an interval, and (b) homeomorphic to the Cantor set.

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Authors and Affiliations

  1. Department of Mathematics, Western Kentucky University, 1906 College Heights Blvd #11078, Bowling Green, KY, 42101-1078, USA

    Jamie Johnson & Tom Richmond

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  1. Jamie Johnson
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  2. Tom Richmond
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Correspondence to Tom Richmond.

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Johnson, J., Richmond, T. Continued radicals. Ramanujan J 15, 259–273 (2008). https://doi.org/10.1007/s11139-007-9076-y

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  • DOI: https://doi.org/10.1007/s11139-007-9076-y

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