Application of the Efros Theorem to the Function Represented by the Inverse Laplace Transform of s−μ exp(−sν)
2021; Multidisciplinary Digital Publishing Institute; Volume: 13; Issue: 2 Linguagem: Inglês
10.3390/sym13020354
ISSN2073-8994
AutoresAlexander Apelblat, Francesco Mainardi,
Tópico(s)Iterative Methods for Nonlinear Equations
ResumoUsing 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 $\mu \ge0$ and $0<\nu<1$ are presented
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