Some articles on laplace series, series:
... Theorem I Given a series of spherical surface harmonics, let Z be a closed set of capacity zero on S and suppose (i) the given series is of class K (ii) and are finite on S-Z where is the continuous ... Theorem II Given a series of spherical surface harmonics, having and upper and lower Poisson sums, respectively, and let Z be a closed set of capacity zero ... Suppose (i) the given series is of class K (ii) and are finite on S-Z (iii) there exists a function defined on S, on S, such that for P on S Then the given series is Poisson summable almost everywhere on S and is the ...
Famous quotes containing the words series and/or laplace:
“Every Age has its own peculiar faith.... Any attempt to translate into facts the mission of one Age with the machinery of another, can only end in an indefinite series of abortive efforts. Defeated by the utter want of proportion between the means and the end, such attempts might produce martyrs, but never lead to victory.”
—Giuseppe Mazzini (18051872)
“Given for one instant an intelligence which could comprehend all the forces by which nature is animated and the respective positions of the beings which compose it, if moreover this intelligence were vast enough to submit these data to analysis, it would embrace in the same formula both the movements of the largest bodies in the universe and those of the lightest atom; to it nothing would be uncertain, and the future as the past would be present to its eyes.”
—Pierre Simon De Laplace (17491827)