## Lagrange Inversion Theorem

Let be defined as a function of in terms of a parameter by

Then any function of can be expressed as a Power Series in which converges for sufficiently small and has the form

References

Goursat, E. Functions of a Complex Variable, Vol. 2, Pt. 1. New York: Dover, 1959.

Moulton, F. R. An Introduction to Celestial Mechanics, 2nd rev. ed. New York: Dover, p. 161, 1970.

Williamson, B. Remainder in Lagrange's Series.'' §119 in An Elementary Treatise on the Differential Calculus, 9th ed. London: Longmans, pp. 158-159, 1895.

© 1996-9 Eric W. Weisstein
1999-05-26