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On a theorem of S. Bernstein

Published online by Cambridge University Press:  24 October 2008

Shih-Hsun Chang
Shih-Hsun Chang
Affiliation:
Institute for Advanced StudyPrinceton, N.J.
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Extract

S. Bernstein (see(l), pp. 198–204) has proved that if

is an entire function of genus zero, then the series

is convergent. By considering the most unfavourable case, when all the (βn) are positive real numbers, and writing

which is convergent by hypothesis, he proved that

.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 48 , Issue 1 , January 1952 , pp. 87 - 92
Copyright
Copyright © Cambridge Philosophical Society 1952

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References

REFERENCES

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