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In Section 2, we have $T_{\omega^k}(s) = \frac{f(s)}{s-\omega^k} = s^{-1} f(s) + s^{-2} f(s) \omega^k + ... + s^{-m} f(s) (\omega^k)^{m-1}$, where we ignore the negative exponents of $s$. We...