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→Statement: I added an alternative representation for the Lagrange inversion theorem that makes it easier to use in some functions, and I fully believe someone might find it useful. Tags: Reverted Mobile edit Mobile web edit |
→Statement: I forgot to add a really important detail about the ___domain of application, sorry for the confusion Tags: Reverted Mobile edit Mobile web edit |
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The theorem further states that this series has a non-zero radius of convergence, i.e., <math>g(z)</math> represents an analytic function of {{mvar|z}} in a [[neighbourhood (mathematics)|neighbourhood]] of <math>z= f(a).</math> This is also called '''reversion of series'''.
There is an alternative representation derived directly from this theorem
<math>g(z)=\sum_{n=1}^{\infty}\frac{z^{n}}{n}\lim_{s\to n}(s-n)\int_{0}^{a}f(t)^{-s}dt</math>
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