 In order to define the Kelvin transform "f"* of a function "f", it is necessary to first consider the concept of inversion in a sphere in R"n" as follows.It is possible to use inversion in any sphere, but the ideas are clearest when considering a sphere with centre at the origin.Given a fixed sphere "S"(0,"R") with centre 0 and radius "R", the inversion of a point "x" in R"n" is defined to be

A useful effect of this inversion is that the origin 0 is the image of formula_2, and formula_2 is the image of 0.