Abstract
This chapter discusses Laplace and Mellin transforms. It presents a supposition that F(x) is a real-valued function defined over 0 ≤ x < ∞ and is of bounded variation in every finite interval [0, R], 0 <R < ∞. The chapter also describes the convergence abscissa, analyticity of a Laplace–Stieltjes transform, inversion formulas for Laplace transforms, the Laplace transform of a convolution, the bilateral Laplace–Stieltjes transform, and Mellin–Stieltjes transforms. The Laplace–Stieltjes transform is regarded as an extension of the power series.
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