Let f(z) = 0 ajzi be the Maclaurin expansion of a function f(z) analytic at the origin. Prove each of the following statements. ajz²i is the Maclaurin expansion of g (z) := ƒ (2²). f (b) Σajczi is the Maclaurin expansion of h(z) := f (cz). (a) (c) Σajz+j is the Maclaurin expansion of H(z) := z" f (z). j=0 (d) a; (z-zo) is the Taylor expansion of G(z) := ƒ (z − zo) around zo. i-0

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