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Analytical inversion of the Laplace transform without contour integration: application to luminescence decay laws and other relaxation functions

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Abstract

Laplace transforms find application in many fields, including time-resolved luminescence. In this work, relations that allow a direct (i.e., dispensing contour integration) analytical calculation of the original function from its transform are re-derived. The results are used for the determination of distributions of rate constants of several relaxation functions, including the stretched exponential and the compressed hyperbolic luminescence decay laws, and the asymptotic power law relaxation function.

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Authors and Affiliations

  1. Centro de Química-Física Molecular, Instituto Superior Técnico, 1049-001, Lisboa, Portugal

    Mário N. Berberan-Santos

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  1. Mário N. Berberan-Santos
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Correspondence to Mário N. Berberan-Santos.

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AMS subject classification: 44A10 Laplace transform

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Berberan-Santos, M.N. Analytical inversion of the Laplace transform without contour integration: application to luminescence decay laws and other relaxation functions. J Math Chem 38, 165–173 (2005). https://doi.org/10.1007/s10910-005-4961-3

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  • DOI: https://doi.org/10.1007/s10910-005-4961-3

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