  The volume of the hive polytope (or polytope of honeycombs) associated with a
Littlewood- Richardson coefficient of SU(n), or with a given admissible triple
of highest weights, is expressed, in the generic case, in terms of the Fourier
transform of a convolution product of orbital measures. Several properties of
this function -- a function of three non-necessarily integral weights or of
three multiplets of real eigenvalues for the associated Horn problem-- are
already known. In the integral case it can be thought of as a semi-classical
approximation of Littlewood-Richardson coefficients. We prove that it may be
expressed as a local average of a finite number of such coefficients. We also
relate this function to the Littlewood-Richardson polynomials (stretching
polynomials) i.e., to the Ehrhart polynomials of the relevant hive polytopes.
Several SU(n) examples, for n=2,3,...,6, are explicitly worked out.
