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arXiv · 0704.2842

Quadrature formulas for the Laplace and Mellin transforms

Rafael G. Campos·Francisco Mejia
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Abstract

A discrete Laplace transform and its inversion formula are obtained by using a quadrature of the continuous Fourier transform which is given in terms of Hermite polynomials and its zeros. This approach yields a convergent discrete formula for the two-sided Laplace transform if the function to be transformed falls off rapidly to zero and satisfy certain conditions of integrability, achieving convergence also for singular functions. The inversion formula becomes a quadrature formula for the Bromwich integral. This procedure also yields a quadrature formula for the Mellin transform and its corresponding inversion formula that can be generalized straightforwardly for functions of several variables.

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Rafael G. Campos, Francisco Mejia. 2007-04-21. Quadrature formulas for the Laplace and Mellin transforms. https://arxiv.org/abs/0704.2842

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