In mathematics, the Lagrange reversion theorem gives series or formal power series expansions of certain implicitly defined functions; indeed, of compositions with such functions.
In 1770, Joseph Louis Lagrange (1736–1813) published his power series solution of the implicit equation for v mentioned above.
[1][2] In 1780, Pierre-Simon Laplace (1749–1827) published a simpler proof of the theorem, which was based on relations between partial derivatives with respect to the variable x and the parameter y.
[3][4][5] Charles Hermite (1822–1901) presented the most straightforward proof of the theorem by using contour integration.
[6][7][8] Lagrange's reversion theorem is used to obtain numerical solutions to Kepler's equation.