Lagrange Reversion Theorem

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

$z=x+yf(z)$

$g(z)=g(x)+\backslash sum\_\{k=1\}^\backslash infty\backslash frac\{y^k\}\{k!\}\backslash left(\backslash frac\backslash partial\{\backslash partial\; x\}\backslash right)^\{k-1\}\backslash left(f(x)^kg\text{'}(x)\backslash right)$

$z=x+\backslash sum\_\{k=1\}^\backslash infty\backslash frac\{y^k\}\{k!\}\backslash left(\backslash frac\backslash partial\{\backslash partial\; x\}\backslash right)^\{k-1\}\backslash left(f(x)^k\backslash right)$

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

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