Dunkl symmetric coherent pairs of the second kind of positive measures

In this contribution we deal with pairs of symmetric linear functionals (u ,v ) ( u , v ) such that the corresponding sequences of monic orthogonal polynomials ₙ(x;u )≥ 0 { P n ( x ; u ) } n ≥ 0 and \ Pₙ(x;v )≥ 0 { P n ( x ; v ) } n ≥ 0 are related by TμPₙ₊₁(x;u )μ ₙ₊₁=Pₙ(x;v )-τ ₙ₋₁Pₙ₋₂(x;v ), τ ₙ₋₁≠ 0, n≥ 2. T μ P n + 1 ( x ; u ) μ n + 1 = P n ( x ; v ) - τ n - 1 P n - 2 ( x ; v ) , τ n - 1 ≠ 0 , n ≥ 2 . Here Tμ T μ is the standard Dunkl operator in one variable. Such a pair of linear functionals is said to be a symmetric Tμ T μ -coherent pair of the second kind. We give a necessary and sufficient condition in order for a pair of symmetric linear functionals to be a Tμ T