Abstract: Let  P(z) be n-degree hyperspherical polinomials,Q(z) be the second stort of hyperspherical functions,E.be an elipse on z-plane.In this paper,we found some inequalitys about P(z) and Q(z) on z-plane,and generalize inequality in paper [2] when α=0 to when a≥0. In addition,we also found two important expressions ofthe relation.

Key words: hyperspherical polinomial, hyperspherical function, Gegenbauer polinomial