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The q-Legendre polynomials can be treated as some special "functions in thequantum 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 theirfurther generalization by introducing a two parameter family of polynomials. Ifthe former family arises from an algebra which is in a sense "q-commutative",the latter one is related to its noncommutative counterpart. We introduce alsoa two parameter deformation of the invariant integral on a sphere.Comment: 14 pages Late

Non-commutative analogues ofq-special polynomials and aq-integral on a quantum sphere