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Reversion of a formal power series

Published online by Cambridge University Press:  26 February 2010

J. A. Tyrrell
J. A. Tyrrell
Affiliation:
King's College, London.
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Extract

If f(z) is a function of the complex variable z, regular in a neighbourhood of z = 0, with f (0) = 0 and f' (0) ≠ 0, then the equation w = f(z) admits a unique solution, regular in some neighbourhood of w = 0, given by

where C is an appropriate contour encircling z = 0. These formulae are well-known, being stages in the proof of the classical reversion † formula

due to Lagrange.

Type
Research Article
Information
Mathematika , Volume 9 , Issue 1 , June 1962 , pp. 88 - 94
Copyright
Copyright © University College London 1962

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References

† We use the word “reversion” rather than “inversion”, to avoid any confusion with the algebraic use of “inverse” when “reciprocal” is meant.