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On the Power Series of an Integral Function having an Exceptional Value

Published online by Cambridge University Press:  24 October 2008

A. Pfluger  and
G. Pólya
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Extract

1. It is known that the distribution of the vanishing coefficients in the power series of an integral function is closely connected with the analytic properties of the function. But the following theorem has apparently not yet been noticed, although simple and elegant both in statement and in proof.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 31 , Issue 2 , April 1935 , pp. 153 - 155
Copyright
Copyright © Cambridge Philosophical Society 1935

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References

REFERENCES

(1) Borel, E., Leçons sur les séries divergentes (2nd ed., Paris, Gauthier-Villars, 1928).Google Scholar
(2) Faber, G., “Bemerkungen zu einem funktionentheoretischen Satz des Herrn Hadamard”, Jahresbericht d. deutsch. Math. Ver. 16 (1907), 285–98.Google Scholar
(3) Pólya, G., “Untersuchungen über Lücken und Singularitäten von Potenzreihen”, 1st part, Math. Zeitschrift 29 (1929), 549–640;Google Scholar
(3) Pólya, G., “Untersuchungen über Lücken und Singularitäten von Potenzreihen”, 2nd part, Annals of Math. (2), 34 (1933), 731–77.Google Scholar