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Power series with non-integral exponents which are Fourier kernels

Published online by Cambridge University Press:  24 October 2008

Charles Fox
Charles Fox
Affiliation:
McGill University, Montreal, P.Q.Canada
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Abstract

Much is known about power series with integral exponents, and, as in the case of the Theta-functions, about series whose exponents are the squares of the natural numbers. About other types of power series little is known. I prove here that a certain power series whose exponents are the square roots of the natural numbers is a symmetrical Fourier kernel.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 57 , Issue 2 , April 1961 , pp. 274 - 280
Copyright
Copyright © Cambridge Philosophical Society 1961

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References

REFERENCES

(1)Bochner, S., and Chandrasekharan, K., Fourier transforms (Princeton, 1949).Google Scholar
(2)Titchmarsh, E. C., Introduction to the theory of the Fourier integral (Oxford, 1937).Google Scholar
(3)Whittaker, E. T., and Watson, G. N., A course of modern analysis, 2nd ed. (Cambridge, 1915).Google Scholar