Journal of Mathematical Chemistry

, Volume 38, Issue 4, pp 629–635 | Cite as

Properties of the Mittag-Leffler Relaxation Function

  • Mário N. Berberan-Santos


The Mittag-Leffler relaxation function, E α (−x), with 0 ≤ α ≤ 1, which arises in the description of complex relaxation processes, is studied. A relation that gives the relaxation function in terms of two Mittag-Leffler functions with positive arguments is obtained, and from it a new form of the inverse Laplace transform of E α (−x) is derived and used to obtain a new integral representation of this function, its asymptotic behaviour and a new recurrence relation. It is also shown that the fastest initial decay of E α (−x) occurs for α =1/2, a result that displays the peculiar nature of the interpolation made by the Mittag-Leffler relaxation function between a pure exponential and a hyperbolic function.


Mittag-Leffler function Laplace transform relaxation kinetics 

AMS (MOS) classification

33E12 Mittag-Leffler functions and generalizations 44A10 Laplace transform 


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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Centro de Química-Física MolecularInstituto Superior TécnicoLisboaPortugal

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