Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §10.5 Power Series, #42 · Calculus · Power & Taylor series

(Inversion of series) If … find coefficients … in … so that…

(Inversion of series) If $f = a_{1} x + a_{2} x^{2} + \dots$ find coefficients $b_{1}, b_{2}$ in $g = b_{1} x + b_{2} x^{2} + \dots$ so that $f (g (x)) = x$ . Compute $b_{1}, b_{2}$ for $f = e^{x} - 1$ , $g = f^{- 1} = ln (1 + x)$ .

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §10.5 Power Series, #42

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