Application of the Efros theorem to the function represented by the inverse Laplace transform of $s^{-\mu }\exp (-s^{\nu })$

Abstract

Using a special case of the Efros theorem which was derived by Wlodarski, and operational calculus, it was possible to derive many infinite integrals, finite integrals and integral identities for the function represented by the inverse Laplace transform. The integral identities are mainly in terms of convolution integrals with the Mittag-Leffler and Volterra functions. The integrands of determined integrals include elementary functions (power, exponential, logarithmic, trigonometric and hyperbolic functions) and the error functions, the Mittag-Leffler functions and the Volterra functions. Some properties of the inverse Laplace transform of $s^{-\mu }\exp (-s^{\nu })$ with $\mu \ge 0$ and $0<\nu <1$ are presented

arXiv comment19 pages, 1 figure

References in corpus (3)

• Exact and explicit probability densities for one-sided Levy stable distributions
• Levy stable distributions via associated integral transform
• The Wright functions of the second kind in Mathematical Physics

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