An extension of the Laplace transform obtained by using Laguerre-type exponentials is first shown. Furthermore, solution Blissard problem means Bell polynomials gives possibility to associate any numerical sequence a Laplace-type depending on that sequence. Computational techniques for corresponding analytic functions, involving polynomials, are derived.

The method of Laplace transforms is used to find the distribution function, mean, and variance of the number of renewals of a renewal process whose inter-arrival time distribution has a rational Laplace transform. Where the Laplace transform is not rational, we use the Padé approximation method. We apply our method to certain examples and the results are compared to those reported by other rese...

This paper develops a novel boundary meshless approach, Laplace transformed boundary particle method (LTBPM), for numerical modeling of time fractional diffusion equations. It implements Laplace transform technique to obtain the corresponding time-independent inhomogeneous equation in Laplace space and then employs a truly boundary-only meshless boundary particle method (BPM) to solve this Lapl...

This study presents the mathematical background which justi es the use of Laplace space in well test analysis. It enables us to perform the whole parameter identi cation (CD; Skin; kh; ...) in Laplace space, or at least gives us a powerful tool to treat the pressure data in order to recognize the model to use for the parameter identi cation in real space. It shows a manner in which the Laplace ...

Summary: We consider the problem of estimating the first k coefficients in a regression equation with k + 1 variables. For this problem with known variance of innovations, the neutral Laplace weighted-average least-squares estimator was introduced in Magnus (2002). We investigate properties of this estimator in the case where the unknown variance is estimated by least squares. We find that the ...