H. Weyl (1946) established a theorem on the important structure for rotational invariants. Biedenharn and Louck in their famous Encyclopedia of Mathematics on Angular Momentum in Quantum Physics (1981) studied the most important case (n=3) of the general theorem in some detail. However, they pointed out in their book: ``Unfortunately, the expression for the general coefficient has not been given in the literature and one has had to work out these invariant polynomials from the definition". We have solved completely the problem raised by Biedenharn and Louck and present the expressions for the coefficients generally and explicitly in this talk.

The paper arXiv-1203-6702-math-ph is in submission.