An article is devoted to a communication of transformation of Laplace with the decision of the task of Dirichlet. With help of integrals of Poisson and Schwartz we obtain an inversion formula of the transformation of Laplace by only positive values of argument. The expression of the sine-transformation of Fourier through the cosine-transformation is found for the functions of hole type. A special decisions of the task of Dirichlet in half-plane is considered.