Lagrange reversion theorem

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This page is about Lagrange reversion. For inversion, see Lagrange inversion theorem.

In mathematics, the Lagrange reversion theorem gives series or formal power series expansions of certain implicitly defined functions; indeed, of compositions with such functions.

Let z be a function of x and y in terms of another function f such that

z = x + yf(z)

Then for any function g,

for small y. If z is the identity

[edit] External links

• Lagrange Inversion [Reversion] Theorem on MathWorld
• Cornish-Fisher expansion, an application of the theorem
• Article on equation of time contains an application to Kepler's equation