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A generalization of the Hurwitz composition theorem to irregular power series

Published online by Cambridge University Press:  24 October 2008

H. G. Eggleston
H. G. Eggleston
Affiliation:
University CollegeSwansea
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Extract

When two functions are given, each with a finite radius of convergence, a theorem due independently to Hurwitz and Pincherle (1, 2) provides information about the position of the singularities of the function

in terms of the positions of the singularities of f(z) and g(z).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 47 , Issue 3 , July 1951 , pp. 477 - 482
Copyright
Copyright © Cambridge Philosophical Society 1951

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References

REFERENCES

(1)Hurwitz, A.C.R. Acad. Sci., Paris, 129 (1899), 350–3.Google Scholar
(2)Pincherle, S.Rend. Accad. Lincei, 8 (1899), 228–32.Google Scholar
(3)Whittaker, E. T. and Watson, G. N.A course of modern analysis (Cambridge, 1915).Google Scholar