Open Access

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

Journal of Inequalities and Applications20082008:656329

DOI: 10.1155/2008/656329

Received: 20 April 2008

Accepted: 22 May 2008

Published: 11 June 2008

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 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.

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Authors’ Affiliations

(1)
Department of Mathematics II, University Politehnica of Bucharest

Copyright

© Antonela Toma. 2008

This article is published under license to BioMed Central Ltd. 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.