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Is there any simple way to prove the Taylor's Expansion Formula of inverse functions ? How Lagrange Inversion Formula can be proven ? Is there any easy way to make it ?

thank you

Since if f(a) = b then f^(-1)(b) = a, it is easy to understand the differences between normal and inverse expansions but I couldn't find a way to show where the coefficient (which contains limit and derivative inside) come from ?

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  • Do you want to prove it by code or what? If not then math.stackexchange.com is more suitable Commented Mar 27, 2023 at 6:24
  • I wonder where the coefficient C_n come from ? C_n = lim_(y->a) d^(n-1)/dy^(n-1) ((y - a) / (f(y) - f(a)))^n. How can C_n coefficient be derived ? Is it a simple way to do it ? Commented Mar 28, 2023 at 7:19
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