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A note on the Wiman–Valiron method

Published online by Cambridge University Press:  20 January 2009

P. C. Fenton
P. C. Fenton
Affiliation:
University of Otago, New Zealand
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Abstract

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Without prior assumptions about growth, fundamental inequalities for the Taylor series of an entire function are obtained, valid outside a certain exceptional set. The results are vacuous or not depending on the estimate for the exceptional set. Only then does the growth of the function enter.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 37 , Issue 1 , February 1994 , pp. 53 - 55
Copyright
Copyright © Edinburgh Mathematical Society 1994

References

REFERENCES

1.Fenton, P. C., Some results of Wiman-Valiron type for integral functions of finite lower order, Ann. of Math. 103 (1976), 237–252.CrossRefGoogle Scholar
2.Fenton, P. C., Wiman–Valiron theory for entire functions of finite lower growth, Trans. Amer. Math. Soc. 252 (1979), 221–232.CrossRefGoogle Scholar
3.Hayman, W. K., The local growth of power series: a survey of the Wiman–Valiron method, Canad. Math. Bull. 17 (1974), 317–358.CrossRefGoogle Scholar
4.Kovari, T., On the Borel exceptional values of lacunary integral functions, J. Analyse Math. 9 (1961), 71–109.CrossRefGoogle Scholar