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

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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Correspondence to Antonela Toma.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Toma, A. Generating Functions for the Mean Value of a Function on a Sphere and Its Associated Ball in . J Inequal Appl 2008, 656329 (2008). https://doi.org/10.1155/2008/656329

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