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E10

[1KZ] Difficulty:*.Let \(g(z)=βˆ‘_{m=0}^∞ b_ m z^ m\) with non-zero radius of convergence \(r_ g\). Let \(I_ gβŠ‚ β„‚\) be a zero-centered disk of radius less than \(r_ g\); so we defined a function \(g:I_ gβ†’β„‚\). We assume \(g(0)=0\) and \(g'(0)β‰  0\). Assuming that the inverse \(f(y)=g^{-1}(y)\) can be expressed in Taylor series \(f(x)=βˆ‘_{n=0}^∞ a_ n x^ n\), compute the coefficients of the series of \(f\) starting from those of \(g\).

Solution 1

[1M0]

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