Articles liés à Integral Transforms and Volterra Functions
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Synopsis
The occurrence of the Volterra functions in the Laplace transformation is associated with the fact that on one hand their Laplace transforms are expressed in terms of the logarithmic functions, and are useful in a determination of many inverse transforms. On the other hand, the operational calculus is a powerful and an efficient method for the derivation of the Volterra function properties. Dealing with the Volterra functions, Humbert, Colombo, Parodi, Barrucand and others assumed that in most cases the functions under consideration are continuous, differentiable and have the Laplace transforms and mathematical operations under the integral sign (e.g. differentiation with respect to variables and parameters, inversion of order of integration and etc.) when applying rules and theorems of operational calculus are permissible. Since the author's main interest lies in the application of the Volterra functions, the same formal approach will be followed here. They suppose that the readers are familiar with the basic properties and techniques of the Laplace transformation which can be easily found in the literature and many others).
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