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Some entire functions with fixpoints of every order

Published online by Cambridge University Press:  09 April 2009

I. N. Baker
I. N. Baker
Affiliation:
Imperial College of Science and Technology, London
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In this paper f(z) will always stand for an entire transcendental function of the complex variable z. For p= 1, 2, … the natural iterate fD(z) of f(z) is defined by These natural iterates are themselves entire transcendental functions; they have been studied by various writers, notably Fatou [3]. References to many papers on iterated will be found in [1].

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 1 , Issue 2 , February 1960 , pp. 203 - 209
Copyright
Copyright © Australian Mathematical Society 1960

References

[1]Baker, I. N., Zusammensetzungen ganzer Funktionen. Math. Zeit. 69, 121–163 (1958).CrossRefGoogle Scholar
[2]Baker, I. N., Fixpoints and iterates of entire functions. Math. Zeit. 71, 146–153 (1959).CrossRefGoogle Scholar
[3]Fatou, P., Sur l'itération des fonctions transcendantes entières. Acta math. 47, 337–370 (1926)CrossRefGoogle Scholar
[4]Nevanlinna, R., Eindeutige analytische Funktionen. 2 Aufl. Berlin, Springer 1953.CrossRefGoogle Scholar
[5]Pólya, G., On an integral function of an integral function. J. London Math. Soc. 1, 12–15 (1926).CrossRefGoogle Scholar
[6]Ullrich, E., Sitzungsberichte preuss. Akad. M. P. Klasse. 1929 (592–608).Google Scholar