Journal of Inequalities and Applications
Volume 2008 (2008), Article ID 656329, 14 pages
Research Article

Generating Functions for the Mean Value of a Function on a Sphere and Its Associated Ball in Rn

Antonela Toma

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.


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.