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On methods of summability based on integral functions

Published online by Cambridge University Press:  24 October 2008

D. Borwein
D. Borwein
Affiliation:
St Salvator's College University of St Andrews
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Extract

Suppose throughout that

and that

is an integral function. Suppose also that l, sn(n = 0,1,…) are arbitrary complex numbers and denote by ρ(ps) the radius of convergence of the series

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 55 , Issue 1 , January 1959 , pp. 23 - 30
Copyright
Copyright © Cambridge Philosophical Society 1959

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References

REFERENCES

(1)Borwein, D.On methods of summability based on power series. Proc. Roy. Soc. Edinb. 64 (1957), 342–49.Google Scholar
(2)Copson, E. T.Functions of a complex variable (Oxford, 1935).Google Scholar
(3)Good, I. J.Relations between methods of summation of series. Proc. Camb. Phil. Soc. 38 (1942), 144–65.CrossRefGoogle Scholar
(4)Hardy, G. H.Orders of infinity (Cambridge, 1910).Google Scholar
(5)Hardy, G. H.Divergent series (Oxford, 1949).Google Scholar
(6)Titchmarsh, E. C.The theory of functions, 2nd ed. (Oxford, 1939).Google Scholar
(7)WŁodarski, L.Propriétés des mèthodes continues de limitation du type de Borel. Bull. Acad. Polon. Sci., Cl. III, 4 (1956), 173–75.Google Scholar