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February 2012 Limits of iterations of complex maps and hypergeometric functions
Keiji MATSUMOTO, Takashi OIKAWA
Hokkaido Math. J. 41(1): 135-155 (February 2012). DOI: 10.14492/hokmj/1330351340

Abstract

We consider the limit of the iteration of a map zm(z) from a complex domain D to D. For two kinds of maps m, we show that each iteration mn(z) of m(z) converges for any zD as n → ∞ and that this limit is expressed by the hypergeometric function. These are analogs of the expression of the arithmetic-geometric mean by the Gauss hypergeometric function.

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Keiji MATSUMOTO. Takashi OIKAWA. "Limits of iterations of complex maps and hypergeometric functions." Hokkaido Math. J. 41 (1) 135 - 155, February 2012. https://doi.org/10.14492/hokmj/1330351340

Information

Published: February 2012
First available in Project Euclid: 27 February 2012

zbMATH: 1253.30039
MathSciNet: MR2931698
Digital Object Identifier: 10.14492/hokmj/1330351340

Subjects:
Primary: 30D05
Secondary: 33C05, 33C65

Rights: Copyright © 2012 Hokkaido University, Department of Mathematics

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Vol.41 • No. 1 • February 2012
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