Generating Functions for the Mean Value of a Function on a Sphere and Its Associated Ball in
© Antonela Toma. 2008
Received: 20 April 2008
Accepted: 22 May 2008
Published: 11 June 2008
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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