  The q-Legendre polynomials can be treated as some special "functions in the
quantum double cosets $U(1)\setminus SU_q(2)/U(1)$". They form a family
(depending on a parameter $q$) of polynomials in one variable. We get their
further generalization by introducing a two parameter family of polynomials. If
the former family arises from an algebra which is in a sense "q-commutative",
the latter one is related to its noncommutative counterpart. We introduce also
a two parameter deformation of the invariant integral on a sphere.
