Abstract
The known interpretation of a two-parameter family of Askey–Wilson polynomials as spherical elements on the $SU(2)$ quantum group is extended to an interpretation of a three-parameter (one discrete parameter) family of Askey–Wilson polynomials as associated spherical elements on the $SU(2)$ quantum group. An abstract addition formula, i.e., an expression involving noncommuting variables, for the two-parameter class of Askey–Wilson polynomials is obtained by this interpretation. Specialization gives an abstract addition formula for the continuous q-Legendre polynomials from which the ordinary Rahman–Verma addition formula for continuous q-Legendre polynomials is obtained.
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