Projection of a spherical distribution and its inversion

A single integral expresses the projection of a spherically (or circularly) symmetric distribution on a space of n dimensions onto a subspace (or plane or line) of m<n dimensions. This transformation is inverted by a derivative of order ( n-m)/2, which, for odd (n-m), is given by a single integral. These relationships are applied to several examples that illuminate the interrelations among a number of classical probability distributions and reveal the probability density function of the angle between a unit n-dimensional vector with uniformly distributed direction and any m-dimensional subspace