  In the field of radial basis functions mathematicians have been endeavouring
to find infinitely differentiable and compactly supported radial functions.
This kind of functions are extremely important for some reasons. First, its
computational properties will be very good since it's compactly supported.
Second, its error bound will converge very fast since it's infinitely
differentiable. However there is hitherto no such functions which can be
expressed in a simple form. This is a famous question. The purpose of this
paper is to answer this question.
