Limits of iterations of complex maps and hypergeometric functions

被引：0

作者：

Matsumoto, Keiji ^{[1
]}

Oikawa, Takashi ^{[2
]}

机构：

[1] Hokkaido Univ, Dept Math, Sapporo, Hokkaido 0600810, Japan

[2] Hokkaido Kushiro Higashi High Sch, Kushiro, Hokkaido 0880618, Japan

来源：

HOKKAIDO MATHEMATICAL JOURNAL | 2012年 / 41卷 / 01期

关键词：

limit of iteration; hypergeometric function; TRANSFORMATION FORMULAS; MEAN ITERATIONS; F-D; AGM;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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

引用

页码：135 / 155

页数：21

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