Integral formulas for the spherical polynomials of a root system of type \(BC_ 2\) (Q1328334)

One of the most important unsolved problems of non-commutative harmonic analysis is the determination of the spherical functions of symmetric spaces. \textit{T. Koornwinder} and \textit{I. Sprinkhuizen-Kuyper} proved the existence of the spherical polynomials \(P_{n,k}^{ (\alpha, \beta, u)}\) in rank 2 [SIAM J. Math. Anal. 9, 457-483 (1978; Zbl 0395.33008)]. The author gives another approach to the determination of the spherical polynomials \(P_{n,k}^{ (\alpha, \beta, u)}\) of a root system of type \(BC_ 2\).