Lagrange inversion theorem: Difference between revisions

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m v2.05 - Fix errors for CW project (Reference before punctuation)
Lambert W function: The page falsely sites a radius of convergence of 4+pi^2, whereas the original paper claims a radius of convergence of (4+pi^2)^1/2. The numerical values are also far off due to this mistake.
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The [[radius of convergence]] of this series is <math>e^{-1}</math> (giving the [[principal branch]] of the Lambert function).
 
A series that converges for <math>|\ln(z)-1|<\sqrt{{4+\pi^2}}</math> (approximately <math>20.58\ldots \cdot 10^{-6}0655 < z < 2112.869\ldots \cdot 10^663</math>) can also be derived by series inversion. The function <math>f(z) = W(e^z) - 1</math> satisfies the equation
 
:<math>1 + f(z) + \ln (1 + f(z)) = z.</math>