17.4 Suppose that, for R R. Let {c} be the Laurent coefficients of in the annulus...

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17.4 Suppose that, for R R. Let {c} be the Laurent coefficients of in the annulus R < || < S. Prove, by considering the expansions of g and h, that 9(z) = c + cnzn (|z| 17.7 Estimating Laurent coefficients. {z Suppose that f is holomorphic in an annulus {: R < || < S}. Let f have Laurent expansion (z) = =-xCnz", where 2ic = (0;r) f(w)wn- dw (R < r < S). Estimating N== in the same way as in 14.7, we have |cn| 17.4 Suppose that, for R R. Let {c} be the Laurent coefficients of in the annulus R < || < S. Prove, by considering the expansions of g and h, that 9(z) = c + cnzn (|z| 17.7 Estimating Laurent coefficients. {z Suppose that f is holomorphic in an annulus {: R < || < S}. Let f have Laurent expansion (z) = =-xCnz", where 2ic = (0;r) f(w)wn- dw (R < r < S). Estimating N== in the same way as in 14.7, we have |cn|