  The Clebsch-Gordan coefficients of the group SU(2) are shown to satisfy new
inequalities. They are obtained using the properties of Shannon and Tsallis
entropies. The inequalities associated with the Wigner 3-j symbols are obtained
using the relation of Clebsch-Gordan coefficients with probability
distributions interpreted either as distributions for composite systems or
distributions for noncomposite systems. The new inequalities were found for
Hahn polynomials and hypergeometric functions
