Let f(z) = Σajzi be the Maclaurin expansion of a function ƒ (z) analytic at the origin. Prove each of the following statements. (a) Σ a¡z²j is the Maclaurin expansion of g(z) := = f (z²). (b) Σajczi is the Maclaurin expansion of h(z) := f(cz). (c) Σ a¡zm+j is the Maclaurin expansion of H (z) := z™ ƒ (z). (d) Laj (z (d) Σaj i=0 (zzo) is the Taylor expansion of G(z) := f (z - zo) around zo.

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