Fourier, Laplace, and Mellin Transforms

12.1–12.4 Integral Transforms

12.11 Laplace transform

The Laplace transform of the function f(x)si1_e, denoted by F(s)si2_e, is defined by the integral

F(s) = 0f(x)esxdx, Re s > 0


The functions f(x)si4_e and F(s)si5_e

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