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On the Asymptotic Periods of Integral Functions

Published online by Cambridge University Press:  24 October 2008

Sheila Scott
Sheila Scott
Affiliation:
Girton College
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Extract

A period of a function f(z) is defined to be a number ω (≠ 0) such that

is identically zero; and it can be shown that an integral function may either have no periods or else a single sequence kλ (k = ± 1, ± 2, …).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 31 , Issue 4 , October 1935 , pp. 543 - 554
Copyright
Copyright © Cambridge Philosophical Society 1935

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References

* Whittaker, J. M., Proc. Edinburgh Math. Soc. 3 (1933), 241–58CrossRefGoogle Scholar; 4 (1934), 77–8.

† Guichard, C., Annales Sci. de l' Ecole Normale, 4 (1887), 361–80.CrossRefGoogle Scholar

* Valiron, G., Integral functions (Toulouse, 1923), p. 41.Google Scholar

* Nörlund, N. E., Sur la “somme” d'une fonction (Paris, 1927), p. 10.Google Scholar

† Ibid., p. 8.

* Nörlund, N. E., Sur la “somme” d'une fonction (Paris, 1927), pp. 7, 8.Google Scholar

* See Titchmarsh, , Theory of Functions, p. 186.Google Scholar

* F., and Nevanlinna, R., Acta Soc. Sci. Fen. 50 (1922), 8.Google Scholar

* See F., and Nevanlinna, R., Acta Soc. Sci. Fen. 50 (1922), 22Google Scholar. Replace the imaginary by the real axis and write ø = θ − π/2.

* Cartwright, M. L., Proc. London Math. Soc. (2), 38 (1933), 158–79 (168)Google Scholar, Theorem III.

* Phragmén, E. and Lindelöf, E., Acta Math. 31 (1908), 381–406.CrossRefGoogle Scholar

* Whittaker, J. M., “On the asymptotic periods of integral functions”, Proc. Edinburgh Math. Soc. 3 (1933), 241–258.CrossRefGoogle Scholar

† Loc. cit. p. 242.