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The Range of a Gap Series

Published online by Cambridge University Press:  20 November 2018

J. S. Hwang
J. S. Hwang*
Affiliation:
Département de Mathématiques, Université de Montréal, Québec, Canada
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Theorem. Letbe a function holomorphic in the disk, wherep is a natural number andIfthen then f(z) assumes every complex value infinitely often in every sector.

The purpose of this note is to prove the above result. To do this, we first observe that from the condition a<∞, we can easily show that the derivative f′(z) satisfying

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 18 , Issue 5 , 01 December 1975 , pp. 753 - 754
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Bagemihl, F. and Seidel, W., Koebe arcs andFatou points of nor mal functions. Comment. Math. Helv. 36 (1961), 9-18.Google Scholar
2. Collingwood, E.F. and Lohwater, A.J., The theory of cluster sets. Cambridge Univ. Press, 1966.Google Scholar
3. Fuchs, W. H. J., Topics in Nevanlinna theory. Proc. of the NRL conference on classical function theory (1970), 1-32.Google Scholar
4. Hardy, G.H. and Littlewood, J.E., A further note on Abel's theorem. Proc. London Math. Soc. 25 (1926), 219-236.Google Scholar
5. Lehto, O. and Virtanen, K.I., Boundary behaviour and normal meromorphic functions. Acta Math. 97 (1957), 47-65.Google Scholar
6. Pommerenke, Ch., Lacunary power series and univalent functions. Michigan Math. J. 11 (1964), 219-233.Google Scholar