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Iterated complex radicals

Published online by Cambridge University Press:  22 September 2016

Peter L. Walker
Peter L. Walker*
Affiliation:
Dept of Mathematics, University of Lancaster, Bailrigg, Lancaster
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Extract

The question of the convergence of the sequence defined recursively by

for a given complex value of c, and a fixed determination of the square root was posed by Ogilvy [3], and partial solutions have been given by Rohde [4] and Gerber [5].

Type
Research Article
Information
The Mathematical Gazette , Volume 67 , Issue 442 , December 1983 , pp. 269 - 273
Copyright
Copyright © Mathematical Association 1983

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References

1. Burckel, R. B., Iterating analytic self-maps of discs, Amer. Math. Monthly. 88, 396–407 (1981).Google Scholar
2. Macintyre, A. J., Convergence of;’, Proc. Amer. Math. Soc. 17, 67 (1966).Google Scholar
3. Ogilvy, C. S., To what limits do complex iterated radicals converge? Amer. Math. Monthly, 77, 388–389 (1970).Google Scholar
4. Rohde, H.-W., Complex iterated radicals, Amer. Math. Monthly, 81, 14–21 (1974).CrossRefGoogle Scholar
5. Gerber, L., Complex iterated radicals, Proc. Amer. Math. Soc. 41, 205–210 (1973).Google Scholar