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Proceedings of the American Mathematical Society

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Valence sequences

Author: A. W. Goodman
Journal: Proc. Amer. Math. Soc. 79 (1980), 422-426
MSC: Primary 30C55
MathSciNet review: 567984
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Abstract: Let $ {V_0},{V_1}, \ldots ,{V_k}, \ldots $ be an infinite sequence of positive integers (where we include $ \infty $ as a possible value for $ {V_k}$). The sequence is called a valence sequence if there is an $ f(z)$ regular in the unit disk such that for each $ k \geqslant 0$ the kth derivative $ {f^{(k)}}(z)$ has valence $ {V_k}$ in E. Most of the results obtained here about valence sequences are obvious, but we prove three theorems about valence sequences that are not trivial.

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