NONCOMMUTATIVE ANALOGS OF Q-SPECIAL POLYNOMIALS AND A Q-INTEGRAL ON AQUANTUM SPHERE

q-Legendre polynomials can be treated as some special 'functions in th e quantum double cosets U(1)\SUq(2)/U(1)'. They form a family (dependi ng on a parameter q) of polynomials in one variable. We get their furt her generalization by introducing a two-parameter family of polynomial s. If the former family arises from an algebra which is in a sense 'q- commutative', the latter one is related to its non-commutative counter part. We also introduce a two-parameter deformation of the invariant i ntegral on a quantum sphere.