Wikipedia:Reference desk/Archives/Mathematics/2007 June 8

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June 8

Inverse Laplace transform by complex analysis

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)

Converting horsepower into amperage

How do I Convert horsepower into amperage?

I don't think you can. Ampere is a measure of current, while horsepower is a unit of Power. --Ybbor^Talk 18:54, 8 June 2007 (UTC)

You may have been thinking watts, which is also a unit of power. According to my calulator widget, 1 horsepower is 745.69987 watts. Friday (talk) 18:56, 8 June 2007 (UTC)

For a known voltage and a purely resistive system, wattage is the product of this and amperage, enabling a numerical connection between amps and HP to be derived. If any reactive elements are present, power is less then volt-amps, of course, and the reactive impedance will depend on the size of capacitative or inductive components in farads or henrys and the frequency of the applied voltage. 86.132.167.202 20:25, 8 June 2007 (UTC)