Abstract
This paper gives some details of the experimental discovery and partial proof of a simple asymptotic development for the largest magnitude roots of the Mandelbrot polynomials defined by p 0(z) = 1 and \(p_{n+1}(z) = zp_{n}^{2}(z) + 1\).
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References
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Acknowledgements
The discussion with Neil Calkin, during the course of the JonFest DownUnder conference, was very helpful. One might even say that had those discussions not taken place, RMC would not have been bitten (by the problem). Peter Borwein pointed out the work of Aczél on functional differential equations. This research work was partially supported by the Natural Sciences and Engineering Research Council of Canada, the University of Western Ontario (and in particular by the Department of Applied Mathematics), the Australian National University (special thanks to the Coffee Gang, Joe Gani, Mike Osborne, David Heath, Ken Brewer, and the other regulars, for their interest), and by the University of Newcastle.
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Communicated By Heinz H. Bauschke.
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Corless, R.M., Lawrence, P.W. (2013). The Largest Roots of the Mandelbrot Polynomials. In: Bailey, D., et al. Computational and Analytical Mathematics. Springer Proceedings in Mathematics & Statistics, vol 50. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7621-4_13
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DOI: https://doi.org/10.1007/978-1-4614-7621-4_13
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