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To find the inverse Laplace transform of F(z) via complex inversion formula, we have to assume |F(z)| <= m/|z|k for all large |z|. Theorem 8.2.1 of J.E. Marsden and M.J. Hoffman, Basic complex analysis, 3rd edition, Freeman, 1999 merely assumes k > 0 and for quotients of polynomials k >= 1. Also A. D. Wunsch, Complex variables, 3rd edition, Addison-Wesley, 2005 assumes nothing more than k > 0 but gives a reference to find a proof. The old book R.V. Churchill, Operational Mathematics, 2nd Ed., ACTUALLY assumes k > 1 in the proof of Theorem 5 of its section 63.
Questions: Where can I find a proof for the case k = 1 or better k > 0? Did I overlook something in the above standard textbooks? Thank you in advance. Twma 06:37, 8 June 2007 (UTC)
How do I Convert horsepower into amperage?