Journal of Inequalities and Applications
Volume 2008 (2008), Article ID 656329, 14 pages
doi:10.1155/2008/656329
Research Article
Generating Functions for the Mean Value of a Function on a Sphere and Its Associated Ball in Rn
Department of Mathematics II, University Politehnica of Bucharest, Splaiul Independenţei 313, 060042 Bucharest, Romania
Received 20 April 2008; Accepted 22 May 2008
Academic Editor: Patricia Wong
Copyright © 2008 Antonela Toma. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We define two functions which determine the properties and the
representation of the mean value of a function on a ball and on its
associated sphere. Using these two functions, we obtain Pizzetti's formula in Rn as
well as a similar formula for the mean value of a function on the ball
associated to the sphere. We also give the expressions of the remainders in these two formulas,
using the surface integral on a sphere.