In mathematical analysis, the Lagrange inversion theorem, also known as the Lagrange–Bürmann formula, gives the Taylor series expansion of the inverse function of an analytic function.
== Theorem statement ==
Suppose z is defined as a function of w by an equation of the form
z
=
f
(
w
)
{\displaystyle z=f(w)}
where f is analytic at a point a and f '(a) ≠ 0. Then it is possible to invert or solve the equation for w, expressing it in the form
w
=
g
(
z
...