Abstract: The initial- value problem of the wave equation in the three-dimensional case

is a very important content in the course of methods of mathematical physics. In this paper，we

discuss the definition of the spherically

averaging function and how to build up the partial differential equation satisfied when we use the

method of spherical means to solve this problem. A more concise procedure to deduce the

equation of spherically averaging function is provided based on the analysis of the

deduction appeared in the textbooks. Our discussion will clarify the basic meaning of the

spherically averaged function and is benefit to the teaching and studying of the method of

spherical means and other solutions to the equations of mathematical physics in three-dimensional

spherical coordinates.

Key words: methods of mathematical physics, initial - value problem of three-dimensional wave equation, method of spherical means, spherically averaged function