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The region of convergence of simple Taylor–Dirichlet series

Published online by Cambridge University Press:  24 October 2008

G. A. Read
G. A. Read
Affiliation:
The Woolwich Polytechnic
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Extract

In several recent papers G. L. Lunc (7, 8, 9, 10, 11) has examined the series

where {mn} is a sequence of positive integers or zeros, and μn > 0, μn ↑ ∞. The discussion has been aimed towards extending results which are well-known for Dirichlet series to series (1) which Lunc has very reasonably called a Taylor–Dirichlet series.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 65 , Issue 3 , May 1969 , pp. 619 - 634
Copyright
Copyright © Cambridge Philosophical Society 1969

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References

REFERENCES

(1)Boas, R. P.Entire functions (New York, 1954).Google Scholar
(2)Gontcharoff, W.Recherches sur les dérivées successives des fonctions analytiques. Ann. Sci. École Norm. Sup. 47 (1930), 1–78.CrossRefGoogle Scholar
(3)Gontcharoff, W.Sur les zeros des dérivées successives des fonctions absolument monotones. Comm. Soc. Math. Kharkoff (4), 7 (1933), 3–8.Google Scholar
(4)Gontcharoff, W.Détermination des fonctions entières par interpolation. Act. Sci. Ind., Paris, no. 465 (1937).Google Scholar
(5)Hayes, N. D.Roots of the transcendental equation associated with a certain difference-differential equation. J. London Math. Soc. 25 (1950), 226–232.CrossRefGoogle Scholar
(6)Lepson, B.On hyperdirichlet series and related questions. Trans. Amer. Math. Soc. 72 (1952), 18–45.CrossRefGoogle Scholar
(7)Lunc, G. L.On series of Taylor–Dirichlet type. Izv. Akad. Nauk. Armjan S.S.R. Ser. Fiz.- Mat. Nauk 14 (2), (1961), 7–16.Google Scholar
(8)Lunc, G. L.An application of Taylor–Dirichlet series to estimating the growth of entire functions. Izv. Ann. Armjan. S.S.R. Ser. Fiz. Mat. Nauk. 14 (5), (1961), 3–8.Google Scholar
(9)Lunc, G. L.On the overconvergence of certain series. Izv. Ann. Armjan S.S.R. Ser. Fiz.- Mat. Nauk. 15 (5), (1962), 11–26.Google Scholar
(10)Lunc, G. L.On the Landau and Pringsheim theorem. Izv. Akad. Nauk. AzerbaǏdžan S.S.R. Ser. Fiz-Mat. Tehn. Nauk. 1 (1963), 73–79.Google Scholar
(11)Lunc, G. L.On the singularities of Taylor–Dirichlet Series. Dokl. Akad. Nauk. S.S.R. 154 (1964), 38–40.Google Scholar
(12)Whittaker, J. M.Interpolatory function theory (Cambridge, 1935).Google Scholar