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Lagrange reversion theorem
- 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 g is the identity
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
10-26-2009 08:16:03
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details