MediumPower & Taylor series

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §10.5 Power Series, #40 · Calculus · Power & Taylor series

(Composition of series) If … and … find the … coefficients of…

(Composition of series) If $f = a_{0} + a_{1} x + a_{2} x^{2} + \dots$ and $g = b_{1} x + b_{2} x^{2} + \dots$ find the $1, x, x^{2}$ coefficients of $f (g (x))$ . Test on $f = 1/ (1 + x)$ , $g = x / (1 - x)$ , with $f (g (x)) = 1 - x$ .

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §10.5 Power Series, #40

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