  Let $\mathcal{T}_{\mu}$ be the Dunkl operator. A pair of symmetric measures
$(u, v)$ supported on a symmetric subset of the real line is said to be a
symmetric Dunkl-coherent pair if the corresponding sequences of monic
orthogonal polynomials $\{P_n\}_{n\geq 0}$ and $\{R_n\}_{n\geq 0}$ (resp.)
satisfy $$
  R_{n}(x)=\frac{\mathcal{T}_{\mu}P_{n+1}
(x)}{\mu_{n+1}}-\sigma_{n-1}\frac{\mathcal{T}_{\mu} P_{n-1}(x)}{\mu_{n-1}},
n\geq 2,$$
  where $\{\sigma_n\}_{n\geq1}$ is a sequence of non-zero complex numbers and
$\mu_{2n}=2n, \mu_{2n-1}= 2n-1+ 2\mu, n\geq 1.$
  In this contribution we focus the attention on the sequence
$\{S_n^{(\lambda,\mu)}\}_{n\geq 0}$ of monic orthogonal polynomials with
respect to the Dunkl-Sobolev inner product $$
  <p,q>_{s,\mu}=<u,pq>+\lambda<v,\mathcal{T}_{\mu}p\mathcal{T}_{\mu}q>, \lambda
>0, \ \ p, \ q \ \in \mathcal{P}.$$
  An algorithm is stated to compute the coefficients of the Fourier--Sobolev
type expansions with respect to $<. , .>$ for suitable smooth functions $f$
such that $f \in\mathcal{W}_2^1(R, u, v, \mu)=\{ f; \ \|f\|_{u}^{2} + \lambda
\| \mathcal{T}_{\mu }f\|_{v}^{2} <\infty\}$. Finally, two illustrative
numerical examples are presented.
