A new form of the Laplace transform is reviewed as a paradigm for an entire class of fractional functional transforms. Various of its properties are discussed. Such transformations should be useful in ...

The definite integral $M(a)\coloneq \frac{4}{\pi}\int_{0}^{\pi /2}\frac{x^{2}dx}{x^{2}+\text{ln}^{2}(2e^{-a}\text{cos}x)}$ is related to the Laplace transform of the ...

From the Maclaurin expansion of a function f̄(p) of the Laplace transform operator p, rational function approximations to f̄(p) are generated by means of a new nonlinear sequence to sequence ...