Abstract
If 𝜙(t) is a given function of the real variable t then the integral (in which p is constant) if convergent, is defined to be the Laplace transform of 𝜙(t). The use of the integral in determining the solutions of certain types of differential equations is now well known; see, for example, Carslaw and Jaeger, Operational methods in applied mathematics (Oxford University Press).
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