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Published online by Cambridge University Press: 26 February 2010
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.
† We use the word “reversion” rather than “inversion”, to avoid any confusion with the algebraic use of “inverse” when “reciprocal” is meant.
