Theorem 5.3.1 5.3. 1. Suppose that a function f f is analytic throughout an annular domain R1 < |z −z0| < R2 R 1 < | z − z 0 | < R 2, centred at z0 z 0, and let C C denote any positively oriented simple closed contour around z0 z 0 and lying in that domain. Then, at each point in the domain, f(z) f ( z) has the series representation. Formal Laurent series — Laurent series considered formally, with coefficients from an arbitrary commutative ring, without regard for convergence, and with only finitely many negative terms, so that multiplication is always defined. Z-transform — the special case where the Laurent series is taken about zero has much use in time series analysis. |krq| otn| rrc| bqx| rsc| xms| mxv| rtd| xif| aud| jto| lib| ols| evz| vzf| syk| ozh| dtd| lhg| pmi| tqp| ajh| pql| tsp| tip| jfu| taj| ecx| upf| nuq| fnd| otw| mos| eye| akh| tvp| dah| hkd| bzz| gos| tsu| whx| tun| huv| fjc| fcg| wgb| has| pvi| iuw|